# Pattern Formation on Alloys by Cluster Ion Beam Irradiation
## 3 Results and Discussion  
### Atomic Description  
First, we compare the two pure substances, Cu and Au. Cu is a lighter element; therefore, it exhibits greater mobility than Au. In Figure 1 we have shown the results after the bombardments for two angles of incidence: 50\({}^{\circ}\) and 70\({}^{\circ}\). Figure 1a,b,i,j show how the mobility of Cu fundamentally affects the horizontal displacement, forming a more extensive wave pulse. The height of the pulse appears similar; however, differences in the vertical displacement are observed, indicating that the number of displaced atoms in the case of Cu is greater. Unlike previous cases, the shape of the ripple is noticeably softened when it comes to an alloy. That is, the wave pulse becomes wider and less tall and deep. The most significant case is the one that corresponds to the surface with the same proportion of atoms (Figure 1e,f). In this case, it is observed how the solid has lost its structure near the impact zone of the clusters; that is, it has undergone an amorphization process. Disorder is introduced by energetic collisions that disrupt the ordered lattice due to local rapid cooling processes and the loss of compositional homogeneity. Instabilities closer to equilibrium, such as localized phase separation, may occur; however, these will be second-order effects [29]. Taking into account this property and the results obtained in other research [28], it seems that the redistribution process is decisive in determining the formation of surface ripples. However, we will soon  
Figure 1: \(xz\) projections of the system after bombardment with clusters for two angles of incidence: 50\({}^{\circ}\) (**a,c,e,g,i**) and 70\({}^{\circ}\) (**b,d,f,h,j**) and a fluence of 10\({}^{16}\) atoms\(\cdot\)cm\({}^{-2}\). The figures correspond to different surface concentrations (at\(\%\) Cu): 0 (**a,b**), 20 (**c,d**), 50 (**e,f**), 80 (**g,h**), 100 (**i,j**). The crystallographic viewing direction is \(<\)100\(>\). The two surface ridges resulting from the bombardment are shown in blue. see that the different quantities involved in the process contradict this statement. If the radial distribution function is analyzed, the maxima are smoothed out, and atoms begin to appear at intermediate distances. The underlying local order is the same, but the structure is lost on a large scale by alteration of local distances. In Figure 1, the structures for concentrations of 35 and 65 at.% Cu have not been represented. The reason is that the wave pulse is very similar in appearance to the case of equal concentration (Figure 1e,f). The only difference is that the amorphization zone is much smaller, especially in the case of 35 at.% Cu, since it does not appear on the side of the groove where the cluster does not hit. This suggests that the greater mobility of Cu induces this phenomenon. In short, although simulation times prevent a detailed statistical study of the results, Figure 1 shows a gradual morphology variation due to concentration changes, confirming the influence of this magnitude. To obtain information on short-range changes in atomic order after the bombardment, we performed a common neighbor analysis (CNA) [30]. Each pair of bonded atoms (separated less than the first minimum of the radial distribution function) can be assigned three indices (klm). The first index \(k\) is the number of neighbors common to both atoms. The second index \(l\) is the number of bonds between these common neighbors. The third index \(m\) is the number of bonds in the longest continuous chain formed by the \(l\) bonds between common neighbors. We took an area surrounding the groove belonging to an _Oxz_ layer and analyzed it by this procedure in the case of the Au substrate bombarded at 50\({}^{\circ}\). We found that 83.3% were bonds (421) characteristic of an fcc lattice and the remaining 12% were bonds (311) characteristic of the contours of an fcc lattice. We repeated the same process for the 50% Au-Cu substrate bombarded at 50\({}^{\circ}\) and found considerable differences.