*2.2.2 When the angle between ionic and damaged atomic momentum vector is greater than 45° (less than 90°)*

We see that atoms can emerge from the surface as a direct result of the second series of binary collisions. Looking at event B in **Figure 5**, we can see that the affected ion or atom must be able to depart the collision point at an angle greater than 45°

**Figure 5.** *Three types of collisions between ions and superficial atoms.*

(relative to the actual direction of movement of the ion). As a result of the secondary impact on the same plane of motion, it should be possible for the lattice atoms to leave the secondary impact point at angles greater than 45°. Since two angles greater than 45° intersect at an angle greater than 90°, this lattice atom has an outward component of motion from the surface and can therefore be emitted.

Further consideration reveals that atoms cannot be pulled out parallel to the surface normal. Such atoms cannot be pulled in the opposite direction of the incident ion. This necessitates two 90° reflections, at least one of which moves the atom 90° in the grid/lattice while acquiring the zero velocity. Atoms with zero velocity cannot be created or ejected. Atomized atoms can be pulled towards the surface with greater force than usual, but this is not the case.

It has been determined that when ions are normally generated at the energy of interest, the sputtered atoms are removed off the surface essentially with a cosine distribution, similar to the evaporated atoms.

This is significant because the most likely emission direction is the exact opposite to the direction of the incident ion. Obviously, the incident ion's energy provided by the incident ion is so arbitrarily dispersed by the multiple collisions before the atom's emission that the incident momentum vector vanishes completely and has no effect on the emission. Note that this result applies only to the regular sputtering events [5].

#### *2.2.3 Interaction at oblique angles*

Bombarding ions can collide with the surface at oblique angles in some instances. In this instance, a basic/fundamental collision between the incident ion and the surface atom is very likely to result from a collision that occurred earlier in time. In the case of diagonal events, the incident momentum vector is found to have a significant

**Figure 6.** *(a) Direct and (b) indirect penetration by ions.*

influence in the emission pattern, with the sprayed atoms being expelled extremely powerfully in the forward direction.

#### **2.3 Direct and indirect penetration by ions**

The large-angle knockout process can be broadly divided into direct and indirect as shown in **Figure 6**. "Direct" means that the surface atoms are knocked out directly by the incident ions and "indirect" means knockoff of surface atoms by incident ions just before scattering from other target atoms near the surface. Only indirect incidence works if the angle of incidence is not very oblique, but direct incidence plays a major role if the angle of incidence is grazing [6].
