Investigation of surface orientation dependent sputtering of Ag

Sputtering of metal surfaces can be both a beneficial phenomenon, for instance in the coating industry, or an undesired side-effect, for instant materials subjected to irradiation. While the average sputtering yields are well known in common metals, recent studies have shown that the yields can depend on the crystallographic orientation of the surface much stronger than commonly appreciated. In this study, we investigate by computational means, molecular dynamics, the sputtering of single crystalline Ag surfaces under various incoming energies. The results at low and high energy are compared to experimental results for single crystalline Ag nanocubes of different orientations. We observe strong differences between the sputtering yields of different surface directions and ion energies. We analyze the results in terms of the atom cluster size of the sputtered materials, and show that the cluster size distribution is a key factor to understand the correspondence between simulations and experiments. At low energies mainly single atoms are sputtered, whereas at higher energies the sputtered material is mainly in atom clusters.


Introduction
Erosion of surfaces on the atomic level during bombardment by energetic particles, i.e. sputtering, has been a known phenomenon for a long time [1,2].Sputtering can be utilized beneficially in several applications, for instance in the coating industry and in surface cleaning.On the other hand, sputtering is also an unwanted effect, especially in fusion power plants, where the wall materials and the divertor will be eroded by the bombardment of energetic particles [3][4][5][6].Therefore, both for * Author to whom any correspondence should be addressed.
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the pros and the cons, it is important to understand the sputtering effects of materials in detail.
Experimental studies of a wide range of target materials and incoming ions have been investigated since the midtwentieth century [7][8][9][10].In these studies the effect of ion species and energy on the sputtering yield of single crystalline, polycrystalline or amorphous materials have been determined.Since pure elemental metals are typically polycrystalline [11] and except for Ga cannot be amorphized in the bulk state [12,13], most experimental studies have been focusing on polycrystalline materials.Therefore, the sputtering yields experimentally obtained are an average over all crystal orientations.It is, however, known that the surface orientation will dramatically affect the sputtering yields [14][15][16].At low energies the surface atomic configuration and surface energy of different orientations will affect the sputtering yields [17,18], and at high energies the channeling effects of ions will lower the sputtering yield dramatically compared to directions that are non-channeling [19].In order to investigate the effect of certain orientations, there have been some systematic studies on the effect of surface orientation dependent sputtering.Recently, the approach of doing sputtering of a polycrystalline material and then determine by electron backscatter diffraction the orientation of different grains [16,20] has enabled studying sputtering of a wide range of orientations in the same experiments.Results of these studies showed a strong dependence of the yield on crystal orientation.
Sputtering has been widely simulated using both the binary collision approximation (BCA) [21,22] and molecular dynamics (MD) [23][24][25] approaches.The most commonly used BCA codes simulate only amorphous material [26][27][28] and are hence not suitable to examine how crystal structure may affect sputtering.Some BCA codes [22,29] and all MD codes can handle crystalline structures.Most MD simulation investigations have been on single crystals at their low index surfaces due to the simplicity of the approach [30][31][32][33][34][35][36].Some MD studies have focused on single crystals, but with random surfaces orientations [18].Simulations have been carried out in a broad range from tens of eV [36] up to hundreds of keV [35].These simulations have shown that the specific surface orientation will affect the sputtering yield, both at low energy as well as high ion energies.At low energies, close to the onset of sputtering, the orientation plays a crucial role and can affect the sputtering by orders of magnitude [36].This is related to the exact atomic configuration at the surface and the respective surface energy.At high ion energies, where channeling is observed [37], the channeling directions can show orders of magnitude lower sputtering yields compared to directions with little or no channeling [20].Simulations have also shown that Sigmund's sputtering yield theory [38], which posits that the energy deposited in the near-surface layers is directly comparable to the sputtering yield, is correct at high energies [20].
The reliability of MD simulations depends crucially on the choice of interatomic potential, which is the main physics input to the method [24].Previous studies that compare several different interatomic potentials for the same sputtering simulations have shown that the results can strongly depend on the interatomic potential [35,39].This obviously brings in a source of uncertainty to the results, but can also be useful for understanding the physics involved behind the sputtering results.As an example of this for another kind of radiation effect, comparing potentials with different melting points have shown that the outcome of radiation effects in the heat spike regime depends clearly on the melting point [40,41].
In this article, we compare simulations with experiments, carried out with a different approach from previous experimental studies [16,20], to examine sputtering over all crystal orientations.Moreover, we extend previous simulation work by also analyzing the sputtering yield results in terms of the atom cluster size of the sputtered materials at several different energies, to understand how grain orientation, ion energy and atom cluster size relate to each other.We also compare results obtained with two different interatomic potentials, which helps to understand how surface energy and cluster binding energy of the materials affect the sputtering.

Molecular dynamics simulations
Two MD simulation programs, PARCAS [42,43] and MDRANGE [44], were used to get the sputtering yield for a wide range of surface orientations for Ga ions impacting silver.The idea of using two simulation tools is to use one to calculate the sputtering yield for a few surface orientations and the other to calculate the energy, which is deposited and transferred (via recoils) to the uppermost 2 nm for the same surfaces.A linear correlation fit between the obtained energy values and the sputtering yields can then be used to estimate the sputtering yield of all orientations [20].We used this method, as the MDRANGE simulations are much faster than the PARCAS simulations, due to the recoil interaction approximation used in it does not calculate sample atom-sample atom interactions [44].
Two different embedded-atom models-type interatomic potentials were used to simulate the interactions between the silver atoms.In this article, they are referenced to as Foiles [45] and CEM [46].The Foiles potential has been previously joined to the Ziegler-Biersack-Littmark (ZBL) [47] repulsive potential in Colla et al [48], to accurately describe the repulsive part.The CEM potential has a realistic repulsive potential built in the original formulation.The Ga-Ag interaction was described by the ZBL repulsive potential [47].
The computer code PARCAS [42,43] was used to simulate the sputtering of Ga ions that impact single crystalline Ag surfaces.These simulations gave values for the sputtering yields for the different surfaces.Four ion energies were used: 2 keV, 8 keV, 20 keV and 30 keV.The number of simulated surfaces and the number of simulations for each surfaces differed between the energies.The number of impacts per surface was determined by the number needed to obtain small enough statistical uncertainty.For the lowest energy, we investigated more surface orientation compared to the higher energies, as it has previously been shown that the linear scaling between sputtering yield and deposited energy falls apart at low impact energy.For 2 keV, 13 surfaces were simulated with each being simulated 2000 times.The surfaces were ⟨100⟩, ⟨101⟩, ⟨102⟩, ⟨111⟩, ⟨112⟩, ⟨104⟩, ⟨2111⟩, ⟨414⟩, ⟨7110⟩, ⟨114⟩, ⟨323⟩, ⟨429⟩, and ⟨7410⟩.For 8, 20 and 30 keV five surfaces were simulated, these being ⟨100⟩, ⟨101⟩, ⟨102⟩, ⟨111⟩ and ⟨112⟩.For 8 keV 5000 simulations were done for each surface while for 20 keV and 30 keV 3000 simulations were done.Each simulation cell consisted of a half sphere with a varying radius.For the 2 keV and 8 keV simulations the half sphere had a radius of 95 Å, for the 20 keV and 30 keV simulations it had a radius of 165 Å.For both cell sizes the outermost atoms around the half sphere were fixed, such that the atoms were kept in the shape of the half sphere.A layer of atoms designated for temperature control was set as an interface between the static and normal Ag atoms.Thus, the amount of free Ag atoms was inside the radius of 87 Å for 2 keV and 8 keV and 157 Å for 20 keV and 30 keV.The surface of the half sphere where the Ga ion impacted on were not affected by the thermostat and were not fixed.
The deposited energy simulations were carried out using the MDRANGE code [44].These simulation take considerably less time than the sputtering simulations, making it possible to calculate the deposited energy for a huge sample of surface directions.A total of 1652 surface directions per energy were calculated, ranging from 0 • to 55 • on the polar axis and from 0 • to 45 • on the azimuthal axis.This made it possible to draw practically continuous heatmaps of the deposited energies, that could then be converted to heatmaps of the sputtering yield by assuming the linear correlation between the two [20].

Experimental
Single crystalline silver nanocubes of about 100 nm size dissolved in ethanol (Sigma-Aldrich, Eschenstr.5, 82 024 Taufkirchen, Germany) having {001} side planes were dispersed on Si(100) substrates via spin coating.All of the single crystalline Ag nanocubes were then oriented normally on the substrates with the ⟨001⟩-axis of the Ag nanocubes being parallel to the substrate normal, which is a necessary condition for all orientation dependent experiments.The single crystalline nature of the Ag nanocubes was checked via high-resolution transmission electron microscopy, and revealed the fcc crystal structure [49].
Ion irradiation was performed in a FEI Helios 600i NanoLab dual-beam focused ion beam system.Various areas of 5 × 3 µ 2 were irradiated with 2, 8, 20, and 30 keV Ga + ions (according to the MD simulations) at an ion fluence of 1.8 × 10 16 ions cm −2 under different polar angles in respect to the substrate normal.The chamber pressure was in the range 4-8 × 10 −6 mbar.The ion beam current was ranging from 15 to 30 pA, depending on the ion energy, resulting in irradiation times varying from about 10-20 s.
Scanning electron microscopy (SEM) images were taken of the Ag nanocubes before and after ion irradiation in the same FEI Helios system with 5 keV electrons and using a backscattered electron detector.The pair of captured SEM images before and after irradiation were individually compared and analyzed with the image analysis software ImageJ [50] in order to determine the volume of each single nanocube before and after irradiation.Full details of this procedure and sample images can be found in the supplementary information of Choupanian et al [49].The sputtering yield Y was then calculated as where ρ at is the atomic density of the target material, ∆V is the volume changes due to the irradiation, ϕ the ion fluence, and A 0 is the average of the cross-section area of the nanocubes before and after the irradiation.The error of the determined sputtering yield varied between 15%-25%, depending on the quality of the SEM images and analysis.For further details see [49].
The SEM images were also used to analyze the orientation of each Ag nanocube with respect to the horizon for the channeling maps.The raw data were interpolated with a 9 th order polynomial function from −45 • to 45 • .These steps were repeated for different directions of the ion beam in respect to the substrate normal (polar angle) from 0 • to 52 • with intervals of 2 • with an accuracy of ± 0.5 • .The results were plotted as a function of polar and azimuthal angles.For further details see [49].

Results
Figure 1 shows the stereographic projection of the fcc crystal, e.g.silver.This triangle between the ⟨100⟩, ⟨101⟩ and ⟨111⟩ axes represents the whole angular space due to the symmetry of the cubic system.We have plotted further axes into the figure for the navigation through the experimental and simulation sputtering results shown in figures 2-5 for the different ion energies.The sputtering yield determined by the simulations for the different interatomic potentials are separated into two separate plots.Thus, together with the experimental sputtering yield, each ion energy has three figures.The color scales are set to 0 at their minimum, while the maximum value is roughly based on the maximum sputtering yield of the experimental results.This enables a direct visual comparison between the different potentials and the experimental values.
The average of the experimental sputtering yield over all directions is about Y ≈ 5, and similar to the simulation values obtained from the CEM potential for an ion energy of 2 keV, as shown in figure 2. However, the Foiles potential does severely overestimate the sputtering yield by roughly 50%.Furthermore, the shape and contour of the graphs, which we also refer as 'channeling maps', between experiment and the simulations are not in a very good agreement.Even though the areas around the ⟨100⟩ and ⟨101⟩ axes do have similar sputtering yields, most of the simulation maps are flat with some minor peaks and higher sputtering yields.Additionally, the broad channeling seen in ⟨101⟩ direction for the simulations is not well represented by the experimental data.
The channeling maps obtained for the ion energy of 8 keV show a much better agreement and are structurally similar, see figure 3. The experimental and simulated results share qualitatively the peaks and valleys, also with similar widths.Even quantitatively, the CEM potential has about the same sputtering yields as the experiment at the ⟨100⟩, ⟨101⟩ and ⟨111⟩ directions.On the other hand, the simulated sputtering yields using the Foiles potential yields double that of the experimental and CEM results.The largest discrepancy between the two is that the CEM potential never shows a sputtering yield over 20 and has a smaller area of high sputtering yield values around the ⟨216⟩ axis.
For an ion energy of 20 keV, figure 4, even more features of the channeling maps between experiment and simulations agree: a clear peak is around the ⟨316⟩ direction, making it a non-optimal channeling direction.A broad valley covers the polar angels above 30 • and below 40 • indicating planar channeling.This valley is smaller for the 8 keV results (figure 3) but still observable, while for the 20 keV it becomes very clear, although a bit narrower experimentally.On the other hand, the sputtering yields from the simulations using the Foiles interaction potential now fits the experimental values, whereas the values from the CEM simulations are a factor of 2 lower.
The experimental and simulated channeling maps also agree on the general shape for an ion energy of 30 keV, as shown in figure 5.The valley between the polar angle of 30 • and 40 • is still present, but even more defined in the experiment.Additionally, the simulated maps show another valley at a polar angle of about 20 • , which has some support from the experimental results.However, it cannot conclusively be confirmed if this is an error from the interpolation or an actual rift between the channeling directions below 30 • .The ⟨316⟩ direction is again a clear non-channeling direction for this ion energy and another peak is emerging corresponding to roughly the ⟨536⟩ direction.The region around the ⟨219⟩ direction also seems to not channel.Besides these agreements, the experimental map has areas yielding values that are 10-15 larger than the simulated ones, and again the CEM potential does underestimate the overall sputtering yield by factor of 2; whereas, the Foiles interaction potential agree for this ion energy with the maximum experimental sputtering yields.
Overall, neither of the potentials show a perfect match with the experimental data across the ion energy range investigated.The CEM potential works clearly better at lower ion energies, while the Foiles works better at higher ion energies.The difference in the sputtering yield stems from the fitting of the slope between the simulated energy deposited in the 2 nm thick surface layer and the simulated sputtering yield at different surface directions.Respective plots are depicted in figure 6.
The Foiles potentials slope (red lines) is always larger than the CEM potential (blue lines), about a factor of two, leading to the higher sputtering values using the Foiles potential.
Next, we analyzed the average size of the sputtered material in order to investigate the differences between the Foiles and CEM interatomic potentials.Typically, single atoms are sputtered away in most cases, if one considers only ballistic collisions, but it has also been proven by both MD simulations and experiments that even large clusters containing hundreds of atoms can leave the surface after ion impact [51][52][53] (the sputtered clusters are hot and on longer time scales, most of them break up into single atoms or smaller clusters [52]).Furthermore, the average potential energy of atoms in silver clusters of different size was determined in order to understand their stability.Both of these results are presented in figure 7.
The mean cluster sizes seen in figure 7(a) clearly shows that the Foiles potential sputters larger clusters than the CEM potential.The average size is above 2 atoms for ion energies of 8, 20 and 30 keV, while ≈1.55 atoms for an ion energy of 2 keV.On the other hand, the CEM potential delivers average cluster sizes between 1.2 and 1.3 atoms per cluster for all investigated energies.A dependence on the surface orientation is more evident for the simulations using the Foiles potential, showing how the directions change the channeling properties with ion energies.This is most evidently seen for the ⟨111⟩ axis, which shows the largest cluster size for an ion energy of 2 keV, but the smallest at 20 and 30 keV.
To further investigate the cluster sizes in the used potentials, the fraction of clusters larger than one atom was calculated, this is seen in table 1.While the fraction tends to increase with the energy, the difference between energies is not large.The largest differences are below 10% and 5% for the Foiles and CEM potentials, respectively, with the largest jump between 2 and 8 keV.The fractions show a very similar pattern to figure 7(a) with a higher fraction corresponding to a higher mean cluster size.Further comparison show that the Foiles fractions are around double that of the CEM, which is also true for the mean cluster size.
The mean potential energies of the silver atoms in different sized clusters are plotted in figure 7(b), as determined from the MD simulations using the two different interatomic potentials (blue & red, left y-axis) together with the difference between them (green data, right y-axis).In general and as expected, the average potential energy is zero for a single atom and rapidly decreases at about ten atoms where it reaches values of −2.2 eV and −1.75 eV for the Foiles and CEM potentials, respectively.Beyond this size the average potential decreases slower until the end at 50 atoms, with the additional decrease being only about 0.5 eV for the CEM and 0.25 eV for the Foiles potential.The difference between the potentials, plotted in green, shows the greatest difference of 0.5 eV for clusters containing 3 and 4 atoms.The difference shrinks as the cluster size increases and stabilizes at a potential energy difference of 0.15 eV.
To understand the reason behind the seen differences, the melting temperature and the surface energies for some surfaces were calculated in both potentials (here the term   surface energy is used in the equilibrium thermodynamic sense as the energy/area needed to form a surface [54], and should not be confused with the only indirectly related surface binding energy concept used in many BCA codes [22,55]).The melting points are 1150 K ± 25 K and 1325 K ± 25 K for the Foiles and CEM potentials, respectively, obtained by the two-phase method [56].The surface energies for the ⟨100⟩, ⟨110⟩, ⟨111⟩ and ⟨112⟩ surfaces were roughly between 600 and 800 mJ m −2 and between 1000 and 1200 mJ m −2 for the Foiles and CEM potentials, respectively.We can see that the Foiles potential show a slightly lower melting point and significantly lower surface energies than the CEM potential.

Discussion
The sputtering yields determined from the MD simulations show a significant dependence on the ion energy.The yield obtained for an ion energy of 2 keV is the lowest, because the total energy deposited by the impacting Ga ions into the Ag surface layer of 2 nm is only 0.8-1.8keV.Furthermore, the contrast in the channeling maps is low for the different directions.Only the minimum yield in the ⟨101⟩ direction is about ≈50% of the maximum seen.However, the channeling maps for 8 keV ions show greater variation and features in the sputtering yields for the different orientation, together with a larger overall sputtering yield.This can also be deduced from figure 6(b) showing significant higher values for the energy deposited in the Ag surface layer with a stronger slope.The channeling maps for the highest ion energies of 20 and 30 keV show similar levels of variation between the orientations, but have an even larger overall sputtering yield.Noteworthy is that the maximum and minimum sputtering yields differ only slightly between 20 keV and 30 keV, while the difference in sputtering yields between 2 keV and 8 keV have a much greater difference.The overall increase in sputtering yield with increasing ion energy is of course due to the increasing total energy transferred to the surface layer, as Sigmunds theory predicts [38].Even though the fraction in relation to the impact ion energy decreases, due to the increasing ion range, the energy deposited into the surface layer peaks between 20-40 keV.This is also the reason why the difference between the 20 and 30 keV channeling maps are minor.The general features of the channeling maps can also be explained by the differences of the deposited energy in the surface layer, as axial directions lead to more or less channeling of the Ga ions depending on the respective Ag lattice plane distances [57].
Analyzing the channeling maps further reveals that although the maximum and minimum sputtering values between 20 and 30 keV only differ slightly for the simulated results, the overall amount of sputtering differs greatly.This is mainly due to more channeling direction, i.e. areas with lower sputtering yield, appearing in the material at 30 keV than at 20 keV.Due to the low variance in sputtering yield at 2 keV, only simple deductions can be done for it, such as that ⟨111⟩ sputter most followed by ⟨100⟩ and ⟨101⟩ having the lowest yield of the three low index surfaces.This changes slightly at 8 keV where the directions around ⟨215⟩ appears to stay non-channeling while the ⟨100⟩ becomes a more channeling surface.The area below ⟨111⟩, around 30 • azimuthal, appears to also stay non-channeling while the corner ⟨111⟩ starts to channel more.Moving to higher energies these nonchanneling areas start to expand and get clearer edges.At 20 keV the area under 30 • azimuthal and 45 • polar grows to cover a wider area with a peak in sputtering yield at ⟨536⟩.The lower non-channeling areas center at ⟨215⟩ does not grow as much, but appears to split in two with a slightly more channeling zone between the two non-changeling areas.The ⟨100⟩ and ⟨101⟩ directions sputter significantly less than the directions with the highest sputtering yield indicating that they are clear channeling directions.The 30 keV simulation channeling map appears very similar to the 20 keV, but with even more defined channeling directions at the low index surfaces and an emerging channeling direction at ⟨112⟩.
Comparing the experimental and simulated results shows very good agreement for the results obtained with ion energies of 8, 20, and 30 keV; however, only limited conclusions can be deduced for the 2 keV case.As mentioned already above, the average sputtering yield of Y ≈ 5 over all directions determined in the experiment indeed agrees best with the simulations using the CEM interatomic potential rather than with the Foiles potential.However, the features of the experimental channeling map do not match at all the simulation maps, which is likely due to the experimental approach.Gallium ions with an ion energy of 2 keV do have only an ion range of ≈2 nm with an straggling of ≈1 nm in silver, as calculated with the stopping and range of ions in matter (SRIM) [27].Given the fact that an ion fluence of 1.8 × 10 16 ions cm −2 is necessary to record the channeling maps, one can easily estimate that the accumulated concentration of Ga atoms in the surface layer is then almost comparable to the number of Ag atoms.Thus, a Ag/Ga surface alloy evolves during the measurement with changing lattice parameters and structure, which might even become polycrystalline under these conditions, and is thus not comparable with our MD simulations.
The trends in the channeling maps determined with higher ion energies are generally the same.The experimental results tend to have a bit larger non-channeling areas compared to the simulated ones, but this can partly be attributed to the resolution of the graphs.Noteworthy also is that the ⟨111⟩ direction is not covered in the experimental maps, but the trend around the direction suggests it to have a similar shape to that of the simulated results.
Looking at the sputtering yields between the two potentials and the experimental results show a fascinating insight, with the 2 and 8 keV experimental sputtering yields having good agreement with the CEM potentials sputtering yield, while at 20 keV and 30 keV the experimental yield agrees much better with the Foiles potentials yield.To find why the potentials perform differently one can study the sputtered atoms and clusters, see again figure 7. From figure 7(b) one sees that the potentials have a notable difference between potential energies of atoms in small clusters.This difference is largest for clusters under 5 atoms, with a peak at 2 to 4 atoms.A lower potential energy between the atoms means that the atoms hold on to each other more tightly, leading to larger clusters sizes.Thus, when sputtering occurs, the sputtered atoms are more often in pairs or larger cluster, rather than singular atoms sputtering by themselves.This is reflected in figure 7(a), where it can be seen that the Foiles potential with its higher cluster binding energy has a larger mean sputtered cluster size compared to the CEM potential.Due to the mean cluster sizes being under 5 atoms, where the largest difference in potential energy is observed, it can be assumed that the potential energy has a large impact on the sputtered clusters and thus also the sputtering yield.A previous study, investigating the crater formation of Au with Xe ions, [35] showed a similar phenomenon, i.e. that one potential showed sputtering of large clusters and the other more single atom sputtering.In that study the potentials were obviously for Au not Ag, but the potentials used were developed by the same groups as the potentials utilized in this study and were developed following the same principles [45,46].This explanation explains why the potentials fit the experimental results at either low or high energies but not both.At low energies (2 and 8 keV), the Foiles potential underestimates the surface energy.This means that it is easy to form new curved surface features, and hence sputter atoms that have first come above the surface.Additionally, the binding energy of clusters will increase the probability of sputtering clusters, further increasing the sputtering yield.When the ion energy is increased, the surface energy difference effect disappears as the ion energy is enough to sputter atoms anyway, and thus it does not matter whether the atoms sputter alone or in pairs, they separate from the surface either way.Compared to the Foiles potential, the CEM potential has lower potential energy between the atoms in clusters, and thus mainly sputters single atoms.The higher surface energy on the other hand means that the atoms have a harder time of getting loose from the surface and thus less sputtering is observed at lower energies.When the ion energy is increased this still holds true, but due to the lower binding energy, the atoms in clusters do not drag other atoms with them when sputtering, leading to a lower sputtering yield than in the experimental results.The difference in melting point is only on the order of 10%, which do not explain the dramatic difference in sputtering yields.However, the surface energies of low index surfaces and the cluster binding energies are substantially different between the potentials, which can explain the seen differences.

Conclusions
We have shown that MD simulations can be used to understand the strong dependence of the sputtering yield on crystal directions in Ag.The sputtering yield correlates well with the energy deposited to the near surface layers, which in turn depends on the crystal orientation analogous to channeling, well in agreement with our accompanying experiments.Via our quantitative theory-experimental approach using different potentials, we could furthermore clearly reveal that at low ion energies mostly single atoms are sputtered, whereas at higher ion energies clusters of atoms are sputtered from the respective surfaces.The cutoff for our particular system of Ga bombardment of Ag is ≈10−15 keV: below, the processes within the collision cascade can be more or less described by ballistic collisions, such as in common MC software packages; whereas, thermal effects must be considered above this cutoff, as done in MD simulations.Such cutoffs should be determined in future also for other material combinations, as this should be considered and has a significant impact for both the beneficial applications of sputtering and the undesired side-effects.
Agreement No 101052200 -EUROfusion).Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission.Neither the European Union nor the European Commission can be held responsible for them.Computer time granted by the IT Center for Science-CSC-Finland and the Finnish Grid and Cloud Infrastructure (persistent identifier urn:nbn:fi:research-infras-2016072533) is gratefully acknowledged.We further thank the Deutsche Forschungsgemeinschaft (DFG) for financial support through the project 'Energy induced nanoparticle substrate interactions' (Ro1198/22-1 and PA925/6-1).

Figure 1 .
Figure 1.Stereographic projection of the fcc crystal, e.g.silver, showing the whole angular space within the triangle of the ⟨100⟩, ⟨101⟩ and ⟨111⟩ axes together with further low and high index axes.

Figure 2 .
Figure 2. Channeling maps/sputtering yield of 2 keV Ga ions on Ag as a function of incident polar and azimuthal angle.(a) Experimental values fitted with a 9th order polynomial function, and MD simulation results using (b) CEM and (c) Foiles interatomic potentials.

Figure 3 .
Figure 3. Channeling maps/sputtering yield of 8 keV Ga ions on Ag as a function of incident polar and azimuthal angle.(a) Experimental values fitted with a 9th order polynomial function, and MD simulation results using (b) CEM and (c) Foiles interatomic potentials.

Figure 4 .
Figure 4. Channeling maps/Sputtering yield of 20 keV Ga ions on Ag as a function of incident polar and azimuthal angle.(a) Experimental values fitted with a 9th order polynomial function, and MD simulation results using (b) CEM and (c) Foiles interatomic potentials.

Figure 5 .
Figure 5. Channeling maps/sputtering yield of 30 keV Ga ions on Ag as a function of incident polar and azimuthal angle.(a) Experimental values fitted with a 9th order polynomial function, and MD simulation results using (b) CEM and (c) Foiles interatomic potentials.

Figure 6 .
Figure 6.Calculated sputtering yields simulated via the MD code PARCAS as a function of the energy, which is deposited in the uppermost 2 nm of a silver surface, as simulated with MDRANGE, for different surface directions (data points).The respective linear fits have been used to determine the full channeling maps for (a) 2 keV, (b) 8 keV, (c) 20 keV, and (d) 30 keV Ga ions impacting silver.

Figure 7 .
Figure 7. (a) Mean cluster size of sputtered material from silver surfaces for all ion energies and five selected orientations for the two different interaction potentials used in the MD simulations.(b) Average potential energy of atoms in clusters as a function of cluster size.

Table 1 .
Average fraction of sputtered clusters larger than one atom.