**4. Results and discussion**

#### **4.1. The low-energy ion scattering by a single and polycrystal surfaces**

The peculiarities and mechanism of the low-energy ion scattering by polycrystal targets were experimentally investigated. In refs. [30, 31], the study of low-energy (*Е* <sup>0</sup> = 80–500 eV) Cs+ and K+ ions scattering on the surfaces of Ta, W, Re and Ti, V, Cr polycrystal surfaces has been performed experimentally and by means of computer simulation method for more accurate definition of the mechanism of scattering and the evaluation of an opportunity to use heavy ions scattering as a tool for surface layers analysis. The angles of incidence *ψ* = 550 and scat‐ tering *θ* = 700 correspond to the specular reflection case. In **Figure 3**, the measured differen‐ tial energy spectra of scattering ions for pairs Cs+ → Ta, Cs<sup>+</sup> → W, Cs<sup>+</sup> → Re, as well as K<sup>+</sup> → Ti, K+ → V, K+ → Cr, in the initial energy range from *E* <sup>0</sup> = 80 to 500 eV, and the target temperature *Т* = 1250 K are shown. Some physical parameters of investigated samples at *μ* > 1 are given in **Table 1**. The same picture can be seen for the case of V, where *E <sup>b</sup>* V = 5.3 eV/ atom, but *E <sup>b</sup>* Ti and *E <sup>b</sup>* Cr are 4.86 and 4.10 eV/atom, respectively.

is 4 × 104

366 Radiation Effects in Materials

the equilibrium lattice sites.

ber of incidence ions [5].

**4. Results and discussion**

. Each new particle is incident on a reset, pure surface. The incident ions and the recoil

atoms were followed throughout their slowing-down process until their energy fell below a predetermined energy: 25 eV was used for the incident ions, and the surface-binding energy was used for the knock-on atoms. The calculations were performed on the crystals comprising up to 120 atomic layers. The simulations were run with the crystal atoms placed stationary at

The initial energy of incident ions was varied from 0.5 to 10 keV, a grazing angle of incidence *ψ* counted from the target surface was 3–30°, and an azimuth angle of incidence *ξ* realized by rotating the target around its normal and counted from the *<*100> direction was 0–180°. The polar scattering angle *θ* was counted from the primary beam direction, the polar escape angle *δ*––from the target surface, and the azimuthal scattering angle *φ*––from the incidence plane. In **Figure 2**, the scattering geometry and scheme of a semichannel on the Cu(100) face along the direction <110> and the target area on it are shown. The impact points on the crystal surface filled a rectangle, whose sides were divided into 100 segments in the beam incidence plane (*I*coordinate) and 1000 segments in the perpendicular direction (*J*-coordinate). The sizes of the target area were 1.28 Ả (half-width of the semichannel) on the *J*-coordinate and 2.56 Ả (the interatomic distance along the <110> row) on the *I*-coordinate. A substantial part of the calculations presented in this chapter was made by the computer simulation technique. This was required by the complexity of the scattering, sputtering, and channeling trajectories and by a large number of correlated collision events which prohibit the use of statistical stochastic methods of calculation. Mathematical experiment is similar in some extent to the physical one,

**Figure 2.** Scheme of ion scattering by a surface semichannel on the Cu(100) face and target area located on it. *I* and *J* are the coordinates of the impact points along and transverse to the semichannel axis, respectively, determining the num‐

The peculiarities and mechanism of the low-energy ion scattering by polycrystal targets were experimentally investigated. In refs. [30, 31], the study of low-energy (*Е* <sup>0</sup> = 80–500 eV) Cs+

**4.1. The low-energy ion scattering by a single and polycrystal surfaces**

while permitting us to extract more information from the latter.

**Figure 3.** Differential energy spectra of Cs+ and K+ ions scattering on corresponding polycrystalline targets at *E* 0 (eV) = 500 (1); 400 (2); 200 (3); 100 (4); 80 (5). Dashed line shows the calculated results under the formula (3).

Here *μ* = *m* 2/*m* <sup>1</sup> is the mass ratio of target atom and ion, respectively. It is seen that the form of spectra in all the cases is similar. It is characterized by a peak in the low-energy range. When *E* <sup>0</sup> decreases, the position of the maxima of energy spectra shifts toward greater relative energy retained by ions. This shift is the smallest in the case of W when the binding energy of target atoms is *E <sup>b</sup>* W = 8.66 eV/atom, and we shall note that for Ta the binding energy is *E <sup>b</sup>* Ta = 8.089 eV/atom and for Re, *E <sup>b</sup>* Re = 8.10 eV/atom.

The position of the maxima in the binary collision approximation (energy of scattered ion retained at single collision with target atom) can be defined approximately as follows [32]:

$$E \, \! / \, E\_o = \left\{ \cos \theta \pm \sqrt{\left( m\_2 \, / \, m\_1 \right)^2 - \sin^2 \theta} \right\} \left\{ \left[ 1 + m\_2 \, / \, m\_1 \right\} \right\}^2 \tag{3}$$

where *E* is the relative energy of the scattering ions which suffered a single binary collision with a target atom (dashed lines in Figure 3), *E* 0 is the energy of primary ions, and *θ* is the angle of scattering. In Figure 3, one can notice the shift of the maxima from the calculated position. As we can see, this shift depends on the binding energy of target atoms and initial energy of scattered ions. Let us note that in case of binary elastic collisions, the energy retained by the scattering ion, at the given angle of scattering, depends on the mass ratio of colliding particles, and the position of the maxima of the energy spectra should be kept constant.


**Table 1.** Some physical parameters of investigated samples at direct mass ratio of colliding particles *μ* > 1.

In **Figure 4a and b**, the dependencies of relative energy retained by scattering ions *E <sup>m</sup>*/*E* 0 in the maximum energy distributions of Cs+ and K+ ions scattered by Ta, W, Re and by Ti, V, Cr polycrystals, respectively, versus the initial energy of impinging ions are presented. It is seen in the whole investigated range of primary energies *E* 0 that the significant growth of relative energy *Em*/*E*0 (where *E*m is the energy of scattering ions in a maximum energy distribution) with *E* 0 decrease is observed. The curves for targets with close values of binding energy *Е <sup>b</sup>* practically coincide, and it may be observed that this growth of relative energy for vanadium and tungsten is flatter. Thus, the least increase in the relative energy of scattered ions *E <sup>m</sup>*/*E* <sup>0</sup> with decrease of initial energy *E* <sup>0</sup> occurs for targets with the largest binding energy *E <sup>b</sup>* ( 8.66 eV/atom for W and 5.3 eV/atom for V), correspondingly. Violation of the binary character of interaction at initial energy decrease began for these pairs at *E* <sup>0</sup> ≈ 200 eV. For other pairs with smaller binding energy of target atoms, this breach began at *E* <sup>0</sup> ≈ 400eV.

atoms is *E <sup>b</sup>*

368 Radiation Effects in Materials

eV/atom and for Re, *E <sup>b</sup>*

**Ions Cs+**

the maximum energy distributions of Cs+

W = 8.66 eV/atom, and we shall note that for Ta the binding energy is *E <sup>b</sup>*

The position of the maxima in the binary collision approximation (energy of scattered ion retained at single collision with target atom) can be defined approximately as follows [32]:

where *E* is the relative energy of the scattering ions which suffered a single binary collision with a target atom (dashed lines in Figure 3), *E* 0 is the energy of primary ions, and *θ* is the angle of scattering. In Figure 3, one can notice the shift of the maxima from the calculated position. As we can see, this shift depends on the binding energy of target atoms and initial energy of scattered ions. Let us note that in case of binary elastic collisions, the energy retained by the scattering ion, at the given angle of scattering, depends on the mass ratio of colliding particles, and the position of the maxima of the energy spectra should be kept constant.

2 2 2

 **(***m***1 = 132.90 a.u.) K+**

 **(***m***1 = 39.10 a.u.)**

ions scattered by Ta, W, Re and by Ti, V, Cr

*m m m m* é ù =± - + ê ú ë û (3)

 q

( )

<sup>0</sup> 2 1 2 1 *E E*/ { cos / sin / [1 / }

Targets Ta W Re Ti V Cr Mass *m* 2 (a.u.) 180.95 183.85 186.20 47.90 50.94 51.99 Mass ratio (*μ* = *m* 2/*m* 1) 1.36 1.38 1.40 1.23 1.30 1.33 Binding energy (eV/atom) 8.09 8.66 8.10 4.86 5.3 4.10 Melting temperature ( °C ) 2996 3387 3180 1660 1900 1857

**Table 1.** Some physical parameters of investigated samples at direct mass ratio of colliding particles *μ* > 1.

smaller binding energy of target atoms, this breach began at *E* <sup>0</sup> ≈ 400eV.

In **Figure 4a and b**, the dependencies of relative energy retained by scattering ions *E <sup>m</sup>*/*E* 0 in

polycrystals, respectively, versus the initial energy of impinging ions are presented. It is seen in the whole investigated range of primary energies *E* 0 that the significant growth of relative energy *Em*/*E*0 (where *E*m is the energy of scattering ions in a maximum energy distribution) with *E* 0 decrease is observed. The curves for targets with close values of binding energy *Е <sup>b</sup>* practically coincide, and it may be observed that this growth of relative energy for vanadium and tungsten is flatter. Thus, the least increase in the relative energy of scattered ions *E <sup>m</sup>*/*E* <sup>0</sup> with decrease of initial energy *E* <sup>0</sup> occurs for targets with the largest binding energy *E <sup>b</sup>* ( 8.66 eV/atom for W and 5.3 eV/atom for V), correspondingly. Violation of the binary character of interaction at initial energy decrease began for these pairs at *E* <sup>0</sup> ≈ 200 eV. For other pairs with

and K+

Re = 8.10 eV/atom.

q

Ta = 8.089

**Figure 4.** Dependencies of relative energy *Em*/*E*0 retained by scattering Cs+ (a) and K+ (b) ions in a maximum of energy distribution versus the initial energy of impinging ions *E* 0.

Formerly, it was shown that the picture represented on Figure 4 occurs also for the cases of heavy Cs+ scattering on the polycrystal surfaces with small atomic masses (Al, Si, Ni) for which the mass ratio of colliding particles is *μ* < 1 [30]. The angles of incidence *ψ* = 450 and scattering *θ* = 900 also correspond to the specular reflection case. In contrast to the results for *μ* > 1, in cases with *μ* < 1, the smallest increase of the relative energy of scattered ions *E <sup>m</sup>*/*E* <sup>0</sup> with decrease of initial energy *E* 0 occurred for the Al target with the smallest binding energy *E <sup>b</sup>*.

In ref. [30], we showed that at an inverse mass ratio of colliding particles (*μ* < 1), for example, Cs+ on Al (*μ* = 0.20), the possible scattering angles considerably exceed a limiting scattering angle in a single collision (*θ* lim = arcsin *μ*). For Cs+ ions scattering on Al target, *θ* lim = 11.7°. This is possible either in the presence of seven or more successive binary collisions of ion with target atoms. This is not probably at that low energy, or at the interaction of an impinging ion Cs+ with the several bonded between each other surface Al atoms simultaneously. The determined correlation between relative energy suffered by scattering ions and binding energy of target atoms confirms such many-particle character of interaction. As established in refs. [30, 31], contrary to the scattering results on targets with direct mass ratio *μ* > 1 (Figure 2), in the cases with inverse mass ratio *μ* < 1 the smallest increase of the relative energy of Cs+ scattered ions *E <sup>m</sup>*/*E* 0 with decrease of initial energy *E* 0 occurs for the Al target with the smallest binding energy (*E <sup>b</sup>* = 3.34 eV/atom; *μ* = 0.20). For Co, Si и Ni targets, binding energies are 4.387, 4.64, and 4.435 eV/atom, correspondingly. In both cases, the curves *E* m/*E* <sup>0</sup> (*E* 0) are placed above each other relative to the binding energies of target atoms to show the influence of binding energy on a process of low-energy ions scattering. There is a correlation between the value of energy change maintained by ions for different values of *E* 0 in the case of scattering by targets with different masses of atoms (for *μ* > 1 and *μ* < 1) and its binding energies. From this contrary behavior between the *E <sup>m</sup>*/*E* 0 (*E* 0) dependencies and the target atom binding energy value *E <sup>b</sup>* for cases with direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles, one can explain the different character of many-particle interaction in these cases [30, 31].

Some physical parameters of the investigated samples at direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles are presented in **Table 2**. The growth of *E <sup>m</sup>*/*E* <sup>0</sup> with *E* <sup>0</sup> decrease, coinciding with the curves for Ta and Re cases in contrast to the scattering by W, as well as the similarity of curves for Ti and Cr cases in contrast to the V case can apparent‐ ly testify to the nonbinary multiparticle nature of interaction of low-energy Cs+ and K+ ions during the scattering by the investigated targets for which *μ* > 1. The contrary behavior of the *E <sup>m</sup>*/*E* 0 (*E* 0) dependencies concerning the target atom binding energy value *E <sup>b</sup>* for cases with direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles testifies to the different character of many-particle interaction in these cases.


**Table 2.** Some physical parameters of investigated samples at direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles.

**Figure 5.** Comparison of experimental energy distribution curves with calculated histograms in the cases of Cs+ and K+ ions scattering by Ta and Ti polycrystals, respectively. *I* (r.u)––intensity of the scattered ions in relative units.

The scattering of Cs+ and K+ ions on experimentally investigated polycrystals was considered on the basis of binary collision approximation by means of computer simulation to assess the experimentally observed fact of the retaining of abnormally great values of relative energy by scattering ions. The calculations were performed using the visualized CASWIN code [33, 34] based on the Monte Carlo simulation method and treating the interaction of ions with a solid surface to be within the binary collision approximation. The Ziegler–Biersack–Littmark and "Kr-C" potentials were used. The surface potential barrier for ions was assumed to be null, and the values of binding energies of surface atoms were taken as mentioned above. The compar‐ ison of calculated results (histograms) with the experiment for K+ –Ti (left) and Cs+ –Ta (right) is given in **Figure 5**. One can see that the agreement became better when *E* 0 increased, which confirms that the binary collision approximation is fair at sufficiently high energies.

Some physical parameters of the investigated samples at direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles are presented in **Table 2**. The growth of *E <sup>m</sup>*/*E* <sup>0</sup> with *E* <sup>0</sup> decrease, coinciding with the curves for Ta and Re cases in contrast to the scattering by W, as well as the similarity of curves for Ti and Cr cases in contrast to the V case can apparent‐

during the scattering by the investigated targets for which *μ* > 1. The contrary behavior of the *E <sup>m</sup>*/*E* 0 (*E* 0) dependencies concerning the target atom binding energy value *E <sup>b</sup>* for cases with direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles testifies to the different

Targets Ta W Re Al Si Ni Mass *m* 2 (a.u.) 180.95 183.85 186.20 26.98 28.09 58.70 Mass ratio (*μ* = *m* 2/*m* 1) 1.36 1.38 1.40 0.20 0.21 0.44 Binding energy (eV/atom) 8.09 8.66 8.10 3.34 4.64 4.435 Melting temperature ( °C ) 2996 3387 3180 660 1420 1452

**Table 2.** Some physical parameters of investigated samples at direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding

**Figure 5.** Comparison of experimental energy distribution curves with calculated histograms in the cases of Cs+

on the basis of binary collision approximation by means of computer simulation to assess the experimentally observed fact of the retaining of abnormally great values of relative energy by scattering ions. The calculations were performed using the visualized CASWIN code [33, 34]

and K+ ions on experimentally investigated polycrystals was considered

ions scattering by Ta and Ti polycrystals, respectively. *I* (r.u)––intensity of the scattered ions in relative units.

 **(***m***1 = 132.90 a.u.)**

and K+

ions

and K+

ly testify to the nonbinary multiparticle nature of interaction of low-energy Cs+

character of many-particle interaction in these cases.

**Ions Cs+**

particles.

370 Radiation Effects in Materials

The scattering of Cs+

With *E* 0 decrease, the maximum of the calculated histogram keeps its position while the experimental curve disposes to the greater relative energy range, significantly at 80 eV. To realize what kind of scattering ions contribute to the peaks observed in the calculated histo‐ grams, each case of multiple scattering was separated.

On the basis of the conducted research, the correlation between the value of energy change maintained by ion for different values of *E* <sup>0</sup> in the case of scattering by targets with different masses of atoms and its binding energies is experimentally established. This correlation indicates considerable influence by the binding of surface atoms to each other on the process of scattering in the low-energy range by polycrystal targets. It is established that low-energy scattering with direct (*μ* > 1) and inverse (*μ* < 1) mass ratios of colliding particles is not described by the mechanism of binary elastic interactions. Summarizing the effects revealed in the present research, such as (i) the disappearing of a structure of energy spectra; (ii) high values of relative energy of scattering ions *E <sup>m</sup>*/*E* 0 and its dependence on initial energy *E* 0; (iii) dependence of scattering ions' energy on binding energy, mass ratio, melting temperature, and packing density of target atoms, one can draw a conclusion about the multiparticle nature of the interaction. The contrary behavior of the *E <sup>m</sup>*/*E* <sup>0</sup> (*E* 0) dependencies concerning the target atom binding energy value *E <sup>b</sup>* for cases with direct (*μ* > 1) and inverse (*μ* < 1) mass ratio of colliding particles testifies to the different character of many-particle interaction in these cases. In order to use ion-scattering as a tool for diagnostics of disturbances of elemental composition and structure on atomic scale, it is necessary to use much higher initial energies (*E* <sup>0</sup> ≥ 1 keV).

### **4.2. Anomalous inelastic energy losses and trajectory effects at small-angle ion scattering by single-crystal surface**

As is known [35], the elastic mechanism of energy losses is dominant in low- and mediumenergy range for ions with atomic numbers *Z* ≥ 10. However, under the specific conditions of correlated glancing ion scattering from the single-crystal surface, the reverse pattern becomes possible where the inelastic mechanism will predominate. The reasons for this are the large number of collisions involved and the fact that small impact parameters cannot be reached along the scattered ion trajectory [5]. Inelastic processes of ion interaction with crystal exhibit the so-called trajectory effects. Basically, this means that inelastic processes and the associated inelastic energy losses depend on the actual trajectory of the scattered particle [36]. It turned out that the relative magnitude of the anomalous energy losses depends on crystal orientation and increases with decreasing initial ion energy. In ref. [37], this effect is related to the mechanism of surface hyperchanneling (SHC) which dominates for very small grazing angles. The present section gives the results of a study of elastic and inelastic energy losses and of the specific features of the ion trajectories appearing in scattering from discrete model potentials on an atomic row, a semi-channel and a channel on the surface of a single crystal at small grazing and scattering angles, as well as of the contribution of the various scattering mecha‐ nisms to the experimentally observed anomalous energy losses [5, 38]. Trajectories of 15 keV Ar+ ions suffering grazing scattering at the atomic chains, semi-channels, and channels on the Cu(100) surface were traced in the uppermost 10 atomic layers by computer simulation. They have been simulated in the binary collision approximation using the Biersack–Ziegler– Littmark interaction potential [35] and with regard to the time integral. In order to consider simultaneous collisions of an ion with several target atoms the procedure proposed in ref. [27] was used. Elastic and inelastic energy losses have been summed along trajectories of scattered ions. The latter one has been calculated on the basis of the Firsov model modified by Kishi‐ nevsky [5] and included into the scattering kinematics. Figure 2 shows schematically a semichannel on a Cu(100) face in the <110> direction and the target area on it. It also identifies the angles used in the computation. The calculations have been performed for target points, covering uniformly (on the *I* and *J* coordinates) all surfaces of target area, where the total number of filling ions is equal to 5 × 104 .

**Figure 6.** Energy distribution histograms of 15 keV Ar+ ions scattered specularly (*θ* = 2*ψ*) from Cu(100) <110> . On the right-hand side, the most characteristic ion trajectories projected in the transverse plane of the <110> semichannel are depicted.

**Figure 6** shows energy distribution histograms for 15 keV Ar+ ions scattered specularly from Cu(100) <110> into a detector with an angular aperture of ±0.5°. The ions scattered along atomic row ridges contribute to the peaks labeled 1. The peaks located to the left and labeled 2–4 correspond to the ions undergoing surface hyperchanneling (SHC) [37]. In the case of trajec‐ tories of type 4, the ions are seen to be focused in the <110> direction, the focus point lying about 0.5 Å above the surface plane. At *ψ* = 4°, the shape of the spectrum undergoes a sub‐ stantial change because of a sharp increase in the number of trajectories of the new type 5, and a decrease of the contribution from type 1–4 trajectories. The figure shows that the ions with type 5 trajectories are focused by surface rows with the focus point lying slightly above the surface, and propagate afterwards in a diverging flux toward the walls of the semi-channel.

The present section gives the results of a study of elastic and inelastic energy losses and of the specific features of the ion trajectories appearing in scattering from discrete model potentials on an atomic row, a semi-channel and a channel on the surface of a single crystal at small grazing and scattering angles, as well as of the contribution of the various scattering mecha‐ nisms to the experimentally observed anomalous energy losses [5, 38]. Trajectories of 15 keV Ar+ ions suffering grazing scattering at the atomic chains, semi-channels, and channels on the Cu(100) surface were traced in the uppermost 10 atomic layers by computer simulation. They have been simulated in the binary collision approximation using the Biersack–Ziegler– Littmark interaction potential [35] and with regard to the time integral. In order to consider simultaneous collisions of an ion with several target atoms the procedure proposed in ref. [27] was used. Elastic and inelastic energy losses have been summed along trajectories of scattered ions. The latter one has been calculated on the basis of the Firsov model modified by Kishi‐ nevsky [5] and included into the scattering kinematics. Figure 2 shows schematically a semichannel on a Cu(100) face in the <110> direction and the target area on it. It also identifies the angles used in the computation. The calculations have been performed for target points, covering uniformly (on the *I* and *J* coordinates) all surfaces of target area, where the total

.

**Figure 6.** Energy distribution histograms of 15 keV Ar+ ions scattered specularly (*θ* = 2*ψ*) from Cu(100) <110> . On the right-hand side, the most characteristic ion trajectories projected in the transverse plane of the <110> semichannel are

number of filling ions is equal to 5 × 104

372 Radiation Effects in Materials

depicted.

Trajectories of type 5 differ in shape and character from SHC trajectories. The sharp increase in their number suggests the existence of a peculiar refocusing effect which results in a pronounced narrowing of the spatial distribution of scattered particles. The angular range where this refocusing effect is observed is small (3.5° ≤ *ψ* < 5°), so that at *ψ* = 5° it is no more. At *ψ* = 5°, in addition to peaks 1–5, new, lower energy peaks 6 and 7 appear in the spectrum. The pattern of particle motion along type 7 trajectories is more complex than that along trajectories of type 6. In the latter case, the part of the trajectory within the channel is shorter, the particle actually crossing it. In their shapes and general patterns, these trajectories do not belong to those typical for subsurface hyperchanneling [37], which were also observed in our calculations. There also exist trajectories of type 8 corresponding to ions which, on overcoming the potential barrier of the semi-channel walls, penetrate into deeper lying layers and thus are not backscattered.

**Figure 7.** Experimental [39] (circles) and calculated [5, 38] (crosses) dependencies of the relative energy losses versus the grazing angle for the case *θ* = 2*ψ* for 15 keV Ar+ ions scattered from Cu(100)<110>; elastic (1) and inelastic (2) contri‐ butions to the total relative energy losses.

**Figure 7** displays experimental [39] and calculated [38] dependencies of the relative energy losses (*E* <sup>0</sup> − *E*)/*E* <sup>0</sup> on the grazing angle for 15 keV Ar+ ions scattered from Cu(100) <110>. Here the circles are the experimental data [39], crosses - calculation [5, 38], 1 - elastic and 2 - inelastic energy losses contributions to the total relative energy losses. The calculated curve was constructed by averaging the losses over the various scattering mechanisms in accordance with their relative contributions to the spectra. As seen from **Figure 7**, the main contribution to the anomalous energy losses comes from inelastic losses. The maximum inelastic energy losses are due to particles with trajectories 5–7, as well as due to those undergoing subsurface hyperchanneling. Thus, the elastic energy losses are considerably smaller than the inelastic ones in a region of glancing scattering. The fact that the inelastic losses exceed the elastic ones for small *ψ* in the medium energy range is due to an increase in the number of collisions and the particle trajectory length in the surface region, as well as to the absence of small impact parameters in the course of scattering. The predominance of the inelastic energy losses should reveal itself in the efficiency of the various inelastic processes accompanying the glancing ion scattering from a single-crystal surface.

#### **4.3. Low-energy ion scattering by atomic steps on the single-crystal surface**

Ion bombardment of a solid surface leads to radiation-induced vacancy defects, atomic steps, and defect clusters, as well as to an atomic scale relief (<100 Å) formation. The concentration and the type of the radiation defects being formed depends upon the experimental conditions

**Figure 8.** Energy distributions of the total number (.......) and ion component (+++++) of the argon particles scattered at the angle *θ* = 30° by the surface of Cu(100)<100> at *ψ* = 7° (a) and 23° (b). The calculated energy positions correspond‐ ing to the scattered ions in the spectra are designated by the solid and dotted vertical lines.

and significantly influences the trajectories, angular and energy distributions, as well as the number of the scattered particles. Moreover, there is a correlation between the defect type, the blocking angles of the reflected beam, and the energy distributions of the scattered particles that allows a determination of the defect type and its surface concentration [2–5]. In ref. [40] the number of step atoms formed on the surface of a single crystal Cu(100) at *T* = 300 K, predamaged by the bombardment with Ar+ ions, with an initial energy of *E* <sup>0</sup> = 10 keV and the current density on the target within the range of 10−6–10−8 Aǎcm−2 has been estimated. Figure 1 shows both the energy distributions of the total number (ions plus neutrals) and the ion component of the argon particles scattered by the Cu(100) surface in the <100> direction for two incidence angles of *ψ* = 7° (a) and 23° (b), and a constant scattering angle of *θ* = 30°. The particles having undergone the quasi-single scattering on the step atom of the monoatomic semi-infinite steps contribute to the peaks 1 and 1' of the spectrum, and the particles reflected by the step atom with the previous or subsequent specular scattering on the ordered atomic chain contribute to the peaks 2 and 2' [40]. Schematically, such trajectories are shown in the top of **Figure 8**. The number of step atoms has been estimated according to the intensity of the quasi-single scattering peaks in the energy spectrum of the total number of the scattered particles at *ψ* = 7° (1) and 23° (1'). In **Figure 9**, these spectra are shown with a solid line.

**Figure 7** displays experimental [39] and calculated [38] dependencies of the relative energy losses (*E* <sup>0</sup> − *E*)/*E* <sup>0</sup> on the grazing angle for 15 keV Ar+ ions scattered from Cu(100) <110>. Here the circles are the experimental data [39], crosses - calculation [5, 38], 1 - elastic and 2 - inelastic energy losses contributions to the total relative energy losses. The calculated curve was constructed by averaging the losses over the various scattering mechanisms in accordance with their relative contributions to the spectra. As seen from **Figure 7**, the main contribution to the anomalous energy losses comes from inelastic losses. The maximum inelastic energy losses are due to particles with trajectories 5–7, as well as due to those undergoing subsurface hyperchanneling. Thus, the elastic energy losses are considerably smaller than the inelastic ones in a region of glancing scattering. The fact that the inelastic losses exceed the elastic ones for small *ψ* in the medium energy range is due to an increase in the number of collisions and the particle trajectory length in the surface region, as well as to the absence of small impact parameters in the course of scattering. The predominance of the inelastic energy losses should reveal itself in the efficiency of the various inelastic processes accompanying the glancing ion

**4.3. Low-energy ion scattering by atomic steps on the single-crystal surface**

Ion bombardment of a solid surface leads to radiation-induced vacancy defects, atomic steps, and defect clusters, as well as to an atomic scale relief (<100 Å) formation. The concentration and the type of the radiation defects being formed depends upon the experimental conditions

**Figure 8.** Energy distributions of the total number (.......) and ion component (+++++) of the argon particles scattered at the angle *θ* = 30° by the surface of Cu(100)<100> at *ψ* = 7° (a) and 23° (b). The calculated energy positions correspond‐

ing to the scattered ions in the spectra are designated by the solid and dotted vertical lines.

scattering from a single-crystal surface.

374 Radiation Effects in Materials

**Figure 9.** Histograms of the angular distributions of Ar+ ions with *E* 0 = 10 keV scattered by the ordered surface of Cu(100)<100> at the incidence angle *ψ* = 7° for *T* = 0 (a) and *T* = 300 K (b).

A possibility of scattering at the angle *θ* = 30° under small (*ψ* < 10°) and large (*ψ* > 20°) incidence angles is conditioned by the fact that the bombardment introduces irregularities into the perfect infinite atomic chain, that is, it becomes finite and is followed with the step-up (a) or down (b). The number of step atoms formed under ion bombardment , and estimated from the peaks 1 and 1' over the energy spectra, with an accuracy of ~30%, proved to be ~2 × 1014 cm−2.

The aim of the present work is to study the influence of surface atomic steps on the angular and energy distributions of scattered ions, and to determine both the spatial extension of the atomic steps on the damaged surface of a single crystal and the distances between them under experimental conditions [40]. For this purpose, the trajectories of the particles scattered by both the ordered part of the surface and the monoatomic steps of different spatial extensions placed upon it have been studied carefully by means of computer simulation [41, 42]. The computer simulation allowed an investigation of the atomic steps effect on the single-crystal surface upon the trajectory features of the ions being scattered along the ridge of the atomic chains and undergoing the surface hyperchanneling and semichanneling as well.

The calculated energies of the particles scattered along trajectories of the 1, 1', 2, and 2' agreed with the experimentally determined positions of the corresponding peaks in the spectrum, namely: *E*/*E* 0 = 0.84 and *E*/*E* <sup>0</sup> = 0.92 (vertical solid lines in Figure1a and b). The ions scattered along the trajectories 2 and 2' before being reflected from the step atom or after it usually underwent 8–10 collisions with the chain atoms. Their range along the surface approximately amounted to 25–30 Å, and the inelastic energy losses were about 20% of the total loss. Broad maxima 3, 4 and 3', 4' between the peaks 1 and 2 as well as 1' and 2' were not explained in ref. [40]. It was suggested in ref. [40] that they could be explained by the particles scattering on the ordered surface, taking into account the thermal vibrations of its atoms. Our calculations have shown, however, that these broad maxima could not be explained in this fashion. In Figure 9, the histograms of the angular distributions of the scattered argon particles at *ψ* = 7° and the target temperature *T* = 0 (a) and *T* = 300 K (b) are shown. As seen, the scattering at angle *θ* = 300 at *ψ* = 7° is not observed upon the ordered surface, because of blocking, even taking into account the thermal vibrations of its atoms. Variations in the interaction potential, and in particular the use of the conjugated Firsov and Born–Mayer potential [43] also did not allow an explanation of scattering at *θ* = 30° and *ψ* = 7°. In order to explain the maxima 3, 4 and 3', 4' in the spectra, we have calculated the trajectories of the ions scattered on the surface, upon which before or after the semi-infinite monoatomic step and isolated steps (atomic fragments) of different extension *l*, separated by the parts of the ordered surface of length *L*, were located. Schematically, such trajectories are shown at the bottom of Figure 8.

The trajectories 3 and 3' contribute to the broad maxima 3, 4 and 3', 4' in the spectra, being formed by two adjacent steps: the particles pass under the first of the steps and then are reflected from the face atom of the second step. The trajectories of quasi-double scattering 4 and 4' on the face atoms of the adjacent steps also contribute to these maxima. In Figure 9, the contributions of the above-mentioned trajectories are designated with vertical dotted lines. It follows from the calculation that the increase of the number of the atoms in the first step (atomic fragment), and consequently, its extension with constant distance between the steps *L* leads to an energy decrease of the ions being scattered along the trajectories of the 3 and 3' type. A change in the number of atoms in the first step (atomic fragment) from one to four allows 3 and 3' type trajectories of the scattered ions to be obtained with energies covering the whole interval for the relative energies of the broad maxima from *E*/*E* 0 = 0.85 to *E*/*E* <sup>0</sup> = 0.90. The steps (atomic fragments) consisting of two and three atoms separated by the parts of the ordered surface of the length *L* = 15–45 Å turned out to be the most likely ones. The scattering on such steps contributes to the area of the broad peaks 3, 4 and 3', 4' maximum (*E*/*E* <sup>0</sup> = 0.86–0.88). The distances between the atomic steps (fragments) vary from a minimum equal to two lattice constants of Cu(100), to ~45 Å. The presence and value of the peaks 2 and 2' in the spectra confirm the existence of the distance between the steps to be within ~25–45Å. The trajectories of the 4 and 4' type have turned out to be weakly sensitive (by energy value) to the distance between the steps, but their probability sharply decreases with the increase of *L*. It is of interest to note that the disappearance of the 2', 3', and 4' peaks in the ion component of the scattered flux at *ψ* = 23° agrees well with the character of the corresponding trajectories. The conclusions concerning the spatial extension of the atomic steps and the distances between them obtained by the use of the conjugated potential turned out to be in good agreement with the results described earlier, obtained by the Biersack–Littmark–Ziegler potential.

The number of step atoms formed under ion bombardment , and estimated from the peaks 1

The aim of the present work is to study the influence of surface atomic steps on the angular and energy distributions of scattered ions, and to determine both the spatial extension of the atomic steps on the damaged surface of a single crystal and the distances between them under experimental conditions [40]. For this purpose, the trajectories of the particles scattered by both the ordered part of the surface and the monoatomic steps of different spatial extensions placed upon it have been studied carefully by means of computer simulation [41, 42]. The computer simulation allowed an investigation of the atomic steps effect on the single-crystal surface upon the trajectory features of the ions being scattered along the ridge of the atomic chains and

The calculated energies of the particles scattered along trajectories of the 1, 1', 2, and 2' agreed with the experimentally determined positions of the corresponding peaks in the spectrum, namely: *E*/*E* 0 = 0.84 and *E*/*E* <sup>0</sup> = 0.92 (vertical solid lines in Figure1a and b). The ions scattered along the trajectories 2 and 2' before being reflected from the step atom or after it usually underwent 8–10 collisions with the chain atoms. Their range along the surface approximately amounted to 25–30 Å, and the inelastic energy losses were about 20% of the total loss. Broad maxima 3, 4 and 3', 4' between the peaks 1 and 2 as well as 1' and 2' were not explained in ref. [40]. It was suggested in ref. [40] that they could be explained by the particles scattering on the ordered surface, taking into account the thermal vibrations of its atoms. Our calculations have shown, however, that these broad maxima could not be explained in this fashion. In Figure 9, the histograms of the angular distributions of the scattered argon particles at *ψ* = 7° and the target temperature *T* = 0 (a) and *T* = 300 K (b) are shown. As seen, the scattering at angle *θ* =

 at *ψ* = 7° is not observed upon the ordered surface, because of blocking, even taking into account the thermal vibrations of its atoms. Variations in the interaction potential, and in particular the use of the conjugated Firsov and Born–Mayer potential [43] also did not allow an explanation of scattering at *θ* = 30° and *ψ* = 7°. In order to explain the maxima 3, 4 and 3', 4' in the spectra, we have calculated the trajectories of the ions scattered on the surface, upon which before or after the semi-infinite monoatomic step and isolated steps (atomic fragments) of different extension *l*, separated by the parts of the ordered surface of length *L*, were located.

The trajectories 3 and 3' contribute to the broad maxima 3, 4 and 3', 4' in the spectra, being formed by two adjacent steps: the particles pass under the first of the steps and then are reflected from the face atom of the second step. The trajectories of quasi-double scattering 4 and 4' on the face atoms of the adjacent steps also contribute to these maxima. In Figure 9, the contributions of the above-mentioned trajectories are designated with vertical dotted lines. It follows from the calculation that the increase of the number of the atoms in the first step (atomic fragment), and consequently, its extension with constant distance between the steps *L* leads to an energy decrease of the ions being scattered along the trajectories of the 3 and 3' type. A change in the number of atoms in the first step (atomic fragment) from one to four allows 3 and 3' type trajectories of the scattered ions to be obtained with energies covering the whole interval for the relative energies of the broad maxima from *E*/*E* 0 = 0.85 to *E*/*E* <sup>0</sup> = 0.90. The steps

and 1' over the energy spectra, with an accuracy of ~30%, proved to be ~2 × 1014 cm−2.

undergoing the surface hyperchanneling and semichanneling as well.

Schematically, such trajectories are shown at the bottom of Figure 8.

300

376 Radiation Effects in Materials

Thus, from the comparison of the results of computer simulation of the scattered particles' trajectories with the experimental energy distributions, one can draw a conclusion that for bombardment of a Cu(100) surface with 15 keV Ar+ ions under the experimental conditions [40], isolated monoatomic steps (fragments) consisting of several atoms (from one to four) are formed upon it. The distances between the steps vary from two lattice constants of Cu(100) to ~45 Å. The most likely ones turned out to be the steps (fragments) consisting of two and three atoms separated by the parts of the ordered surface of the length *L* = 15–45 Å. The estimated value for the number of the atomic steps calculated by us on the basis of the proposed model of the damaged surface agrees with the value ~2×1014 cm−2 obtained in ref. [40].

#### **4.4. Small angle ion scattering by structures on the single-crystal surface corresponding to the initial stages of adsorption**

Determination of equilibrium position of adatoms, initial stages of adsorption, and the structure of submonolayer adsorption coverages on crystal surfaces are fundamental problems of surface physics. Along with low-energy electron diffraction (LEED), alternative methods are being developed for analysis, in particular ion scattering spectroscopy (ISS) [4, 5, 44]. An attractive peculiarity of the ISS method is its high surface sensitivity, enabling monolayer analysis. The structural analysis of surfaces by this method is based on a comparison of experimentally measured energy and angular distributions of scattered particles with calcu‐ lations based on a chosen surface model. In this section, small-angle scattering of He+ and Ne + ions with initial energies *E* 0 = 1–5 keV and grazing angles within the interval *ψ* = 7.5–15° by Ni(100) <100> single-crystal surface with submonolayer coverages by oxygen or deuterium atoms have been studied. The dynamics of changes of angular and energy distributions from scattering on different adsorption structures, corresponding to the initial stages of adsorption have been studied.

Besides the usual atomic chain effect [5] corresponding to the direct mass ratio of colliding particles, that is, to cases where the mass of projectile *m* 1 is less than that of an atom in the chain *m* 2, in our case a situation arises where an adatom is lighter than the projectile ion. The atomic chain effect manifests itself in this case in a number of features associated with the existence of a limiting scattering angle *θ* lim = arcsin (*m* 2/*m* 1) in quasi-single (QS) and quasidouble (QD) collisions, as well as with the fact that scattering at a given angle *θ* < *θ* lim is possible for two values of the impact parameter *p* [5, 45]. Oxygen atoms on a metal surface at submo‐ nolayer coverages and *T* < 300 K may be adsorbed in two stages––chemisorption and oxidestate. It has been known for many years from LEED [44] that two ordered surface structures can be obtained during the chemisorption of oxygen on Ni(100). A p(2 × 2)–O pattern is obtained at low coverages (one adsorbed oxygen atom for four nickel atoms on the first substrate plane). The saturation of the adsorption corresponds to one adsorbed atom for two nickel atoms and is associated with a c(2 × 2)–O pattern. For our p(2 × 2)–O and c(2 × 2)–O on Ni(100) calculations, we place the O atoms in the fourfold center sites at a distance 0.9 ± 0.1 Å above the Ni surface plane as found in LEED analysis [44] (**Figure 10a–c**).

**Figure 10.** Position of Ni atoms in the first layer of Ni(100) (a) and oxygen atoms in adsorption structures, correspond‐ ing to initial stages of adsorption: (b) p(2 × 2); (c) c(2 × 2); (d) NiO(100) (1 × 1).

Adsorption structures p(2 × 2)–O and c(2 × 2)–O on the Ni(100) surface form sequentially and do no lead to substrate reconstruction [44]. At further increase in oxygen exposure and a coverage degree of 0.62, NiO(100)–(1 × 1) oxide islands begin to form with the NaCl type structure (Figure 1(d)). At the initial stages, this process is interpreted as a phase transition of the first order, and unlike chemisorption it is accompanied by a shift of substrate atoms. In Figure 11, histograms of energy distributions of Ne+ ions, experiencing specular scattering on chains of atoms on a clean Ni(100)<100> surface and on surfaces with different adsorption structures are presented. The acceptance of the analyzer collecting scattered particles, consti‐ tuted by polar and azimuthal scattering angles is Δ*θ* = Δ*φ* = ±0.5°. In a case of a clean surface (**Figure 11a**), the usual peaks of QS- and QD-scattering (1,2) are observed. At specular scattering on the structure p(2 × 2)–O (**Figure 11b**), three peaks, two of which (3 and 4) are of peaks of QS-scattering on oxygen atoms with impact parameters *p*, smaller and larger *p* lim accordingly are present in the spectrum. Here *p* lim (*E* 0) is the impact parameter corresponding to scattering at a limiting angle.

existence of a limiting scattering angle *θ* lim = arcsin (*m* 2/*m* 1) in quasi-single (QS) and quasidouble (QD) collisions, as well as with the fact that scattering at a given angle *θ* < *θ* lim is possible for two values of the impact parameter *p* [5, 45]. Oxygen atoms on a metal surface at submo‐ nolayer coverages and *T* < 300 K may be adsorbed in two stages––chemisorption and oxidestate. It has been known for many years from LEED [44] that two ordered surface structures can be obtained during the chemisorption of oxygen on Ni(100). A p(2 × 2)–O pattern is obtained at low coverages (one adsorbed oxygen atom for four nickel atoms on the first substrate plane). The saturation of the adsorption corresponds to one adsorbed atom for two nickel atoms and is associated with a c(2 × 2)–O pattern. For our p(2 × 2)–O and c(2 × 2)–O on Ni(100) calculations, we place the O atoms in the fourfold center sites at a distance 0.9 ± 0.1 Å

**Figure 10.** Position of Ni atoms in the first layer of Ni(100) (a) and oxygen atoms in adsorption structures, correspond‐

Adsorption structures p(2 × 2)–O and c(2 × 2)–O on the Ni(100) surface form sequentially and do no lead to substrate reconstruction [44]. At further increase in oxygen exposure and a coverage degree of 0.62, NiO(100)–(1 × 1) oxide islands begin to form with the NaCl type structure (Figure 1(d)). At the initial stages, this process is interpreted as a phase transition of the first order, and unlike chemisorption it is accompanied by a shift of substrate atoms. In Figure 11, histograms of energy distributions of Ne+ ions, experiencing specular scattering on chains of atoms on a clean Ni(100)<100> surface and on surfaces with different adsorption structures are presented. The acceptance of the analyzer collecting scattered particles, consti‐ tuted by polar and azimuthal scattering angles is Δ*θ* = Δ*φ* = ±0.5°. In a case of a clean surface (**Figure 11a**), the usual peaks of QS- and QD-scattering (1,2) are observed. At specular scattering on the structure p(2 × 2)–O (**Figure 11b**), three peaks, two of which (3 and 4) are of peaks of QS-scattering on oxygen atoms with impact parameters *p*, smaller and larger *p* lim

ing to initial stages of adsorption: (b) p(2 × 2); (c) c(2 × 2); (d) NiO(100) (1 × 1).

above the Ni surface plane as found in LEED analysis [44] (**Figure 10a–c**).

378 Radiation Effects in Materials

**Figure 11.** Histograms of energy distributions of 5 keV Ne+ ions, undergoing specular scattering on a clean Ni(100) surface (a) and one covered by adsorption structures of oxygen p(2 × 2) (b) and c(2 × 2) (c), as well as on nickel oxide NiO (d). The sliding angle is *ψ* = 12.5°.Typical trajectories of scattered ions numbered 1'–10', contributing to corre‐ sponding peaks (1–10) are schematically presented.

Two peaks of the QS-scattering of ions on lighter adatoms were observed experimentally in ref. [46]. The third peak (5) is provided by QD-scattering on oxygen adatoms. In the energy spectrum for structure c(2 × 2)–O (Figure 12c), peaks of QS- and QD-scattering (6,7) on oxygen atoms with impact parameters *p* larger than *p* lim are presented. The energy distribution of ions scattered on nickel oxide (Figure 2d) differs greatly from the distributions for chemisorption structures (Figure12b and c): peaks 8 and 10 correspond to QS0 scattering from oxygen and nickel atoms, and peak 9 between them correspond to QD-scattering from oxygen and nickel atoms. The analysis of the calculated spectra follows the fact that a number, intensity, and position of peaks on energy scale, corresponding to scattering on different adsorption struc‐ tures, are different, which gives an opportunity to interpret them by means of comparison with experimental spectra. In **Figure 12**, calculated angular distributions of Ne+ ions with *E* 0 = 5 keV and *ψ* = 12.5°, scattered from a clean Ni(100)<100> surface and one covered by different adsorption structures of oxygen are presented. In the case of a clean surface, the usual twopeak structure of angular distribution is observed [4, 5]. With the transition to the p(2 × 2)–O structure (**Figure 12b**), angular distribution of scattered ions changes considerably: it broadens to both sides, and in addition to the peaks observed from a clean surface, a peak appears at a limited angle of scattering from oxygen adatoms *θ* = *θ* lim = 52.5° and a peak of oxygen recoil atoms at θ = 78° (hatched part). The peak at *θ* lim is provided by rainbow scattering, and its position on the angular scale gives an opportunity to identify the type of adatoms by the formula *m* 2 = *m* 1+ sin *θ* lim.

**Figure 12.** Angular distributions of 5 keV Ne+ ions and *ψ* = 12.5°, scattered on a clean Ni(100)<100> surface (a) and covered by adsorption structures of oxygen p(2 × 2) (b) and c(2 × 2) (c), as well as nickel oxide NiO (d). The hatched field in the distribution for the structure p(2 × 2) is the contribution of primary knocked out oxygen adatoms.

Oxygen recoil adatoms are formed by the mechanism of direct knockout, and its detection allows the determination of the type of adsorbate and adsorption stage. At further exposure to oxygen and formation of c(2 × 2)–O chemisorption structure on the Ni(100) surface (**Figure 12c**), peaks at *θ* lim and oxygen recoil atoms disappear. This is connected with the impossibility of QS-collisions of Ne+ ions with oxygen adatoms with impact parameters *p* < *p* lim and releasing of recoil adatoms outside. The angular distribution as a whole narrows in comparison with the distribution for previous structures, testifying to the formation of a denser adsorption structure. On the formation on the surface of nickel oxide, the angular distribution of scattered ions (Figure 12d) also changes: the main structure of the distribution (three peaks) is located in a narrow field and has a background, spreading out to 180°. Such sharp broadening of the distribution is the characteristic feature for scattering on chains, consisting of different sort atoms. Thus, peculiarities of the chain effect at direct and inverse mass ratio of colliding particles and rainbow effect at QS- and QD-scattering of ions, heavier than adatoms lead to the appearance of characteristic peaks in the energy and angular distributions of ions, undergoing small-angle correlated scattering on chains of adatoms and target atoms. Analysis of these peaks and comparison with experiment give an opportunity to control the initial stages of adsorption and identification of adsorption structures with the help of low-energy ion scattering.

### **4.5. Investigation of the dynamics of changes of the Cu3Au(100) surface in the course of ordering by low-energy ion scattering**

Cu3Au(100) single crystal exhibits an order–disorder phase transition into the bulk at *T <sup>c</sup>* = 663 K. This bulk transition is first-order. Theoretically it is predicted that the transition at the surface is of a different type than in the bulk [47, 48]. The transition at the surface has been intensively studied in recent years, including by time-of flight-ion scattering spectroscopy (TOF-ISS) method [49, 50]. In ref. [49] has been shown how the order–disorder transition modifies the atomic sequences in atomic rows, then changing the double-scattering conditions. The atomic row effect exhibits remarkable features in small-angle ion scattering from a singlecrystal surface of complex composition when the rows in certain crystallographic directions consist of alternating atoms of different species. In this section Cu3Au(100) alloy surface has been investigated with low-energy ion scattering at temperatures below and above the bulk order–disorder transition temperature [51].

**Figure 12.** Angular distributions of 5 keV Ne+

380 Radiation Effects in Materials

ions and *ψ* = 12.5°, scattered on a clean Ni(100)<100> surface (a) and

covered by adsorption structures of oxygen p(2 × 2) (b) and c(2 × 2) (c), as well as nickel oxide NiO (d). The hatched field in the distribution for the structure p(2 × 2) is the contribution of primary knocked out oxygen adatoms.

Oxygen recoil adatoms are formed by the mechanism of direct knockout, and its detection allows the determination of the type of adsorbate and adsorption stage. At further exposure to oxygen and formation of c(2 × 2)–O chemisorption structure on the Ni(100) surface (**Figure 12c**), peaks at *θ* lim and oxygen recoil atoms disappear. This is connected with the impossibility of QS-collisions of Ne+ ions with oxygen adatoms with impact parameters *p* < *p* lim and releasing of recoil adatoms outside. The angular distribution as a whole narrows in comparison with the distribution for previous structures, testifying to the formation of a denser adsorption structure. On the formation on the surface of nickel oxide, the angular distribution of scattered ions (Figure 12d) also changes: the main structure of the distribution (three peaks) is located in a narrow field and has a background, spreading out to 180°. Such sharp broadening of the distribution is the characteristic feature for scattering on chains, consisting of different sort atoms. Thus, peculiarities of the chain effect at direct and inverse mass ratio of colliding particles and rainbow effect at QS- and QD-scattering of ions, heavier than adatoms lead to the appearance of characteristic peaks in the energy and angular distributions of ions, undergoing small-angle correlated scattering on chains of adatoms and target atoms. Analysis

**Figure 13.** (a) Ovals of Ar+ ion energy dependence on scattering angle *θ* and angular distributions at scattering from <110> atomic rows on Cu(100)-chain curve; Au(100)-broken curve, and Cu3Au(100)-full curve; (b) Same dependencies for cases where one of the alloy atoms occurs twice in the row.

At temperatures *T* > *T <sup>c</sup>*, all lattice sites are populated uniformly by atoms of both species, while at lower temperatures nonuniform occupation of sites by atoms of different species is typical. Note that <100> rows contain either only Cu or only Au atoms, whereas in the <110> rows the Cu and Au atoms alternate. **Figure 13a** presents ovals depicting the dependence of the energy of scattered Ar+ ions with initial energy *E* 0 = 5 keV on the scattering angle *θ*, which consist of quasi-single (QS)––1 and quasi-double (QD)––2 scattering branches. Shown in the bottom panel are the corresponding angular distributions of ions scattered from <110> rows in the Au(100), Cu(100), and Cu3Au(100) planes. The dashed ovals correspond to the Au atoms, the chain one to the Cu atoms, and the solid oval with a characteristic break (3) to a row of alternating Cu and Au atoms. In the case of a mixed row, the oval has an unusual shape in that the QD branch is replaced by quasi-triple scattering (3) from a sequence of Au–Cu–Au atoms with the principal deflection from the Cu atom which results in considerable energy losses. The QS- and QD-scattering occur in this case primarily from Au atoms. The angular distribu‐ tion contains in the region, corresponding to the break in the oval, an additional maximum and exhibits a dramatic broadening. The maximum appears as a shoulder at *ψ* = 15°, grows with increasing grazing angle, and exceeds in height at *ψ* = 19° the maxima at the limiting scattering angles. As follows from the calculation, the additional maximum comes from the rainbow effect associated with the enhanced scattering close to the shadow-cone boundary of the Au atom toward the nearest Cu atom in a narrow impact parameter region along the row.

**Figure 13b** shows also the scattering ion energy versus the scattering angle ovals and the corresponding angular distributions; however, in this case, in the alternating sequence of atoms, one of them, either Au or Cu occurs twice in succession. Both the energy ovals and the angular distributions are seen to vary dramatically. It is shown when two neighboring atoms belong to the same species, the characteristic break (3) transforms into an additional oval which lies lower than the principal one and corresponds to QS- and QD-scattering from a pair of Cu atoms. To this oval correspond two additional maxima in the angular distribution. A similar pattern is also observed in the case when two Au atoms adjoin one another in a mixed row. The relative height of the additional maxima was found to depend on the number of neigh‐ boring atoms of the same species in a row. Increasing the number of neighboring identical atoms up to three or more results in an increase of the corresponding additional maxima in the angular distribution. Note that the shape of the energy oval and the interval of possible scattering angles are retained, whereas relative height of the maxima at the limiting scattering angles decrease. The characteristic structure of the angular distribution with the number of maxima is also retained when thermal vibrations of atoms in the alloy are included. Thus, a comparison of the angular and energy distributions of ions scattered from the surface of an alloy in the process of ordering with similar distributions for pure targets made up of the alloy components permits a conclusion that two or more neighboring atoms in an alternating sequence are of the same species. The results obtained can be used to study a short-range order in alloys undergoing ordering.

#### **4.6. Ion sputtering of single-crystal surfaces**

In this section, the grazing ion sputtering processes of Si(001), SiC(001), and Cu3Au(001) surfaces at 0.5–5 keV Ne+ bombardment have been studied by computer simulation [52, 53]. Sputtering has been simulated in the primary knock-on regime. Only the primary knock-on recoil (PKR) atoms ejected from first, second, and third layers have been considered. The presence of planar potential energy barrier on the surface was taken into account. The number of incident ions is 4 × 104 . Each new particle is incident on a reset, pure surface. The incident ions and the recoil atoms were followed throughout their slowing-down process until their energy falls below a predetermined energy: 25 eV was used for the incident ions, and the surface-binding energy was used for the knock-on atoms. The calculations were performed on the crystals comprising up to 120 atomic layers. The initial energy of incident ions was varied from 0.5 to 5 keV, an angle of incidence *ψ* counted from target to the surface was 0–30°, and an azimuthal angle of incidence *ξ* realized by rotating the target around its normal and counted from the *<*100> direction was 0–180°.

At temperatures *T* > *T <sup>c</sup>*, all lattice sites are populated uniformly by atoms of both species, while at lower temperatures nonuniform occupation of sites by atoms of different species is typical. Note that <100> rows contain either only Cu or only Au atoms, whereas in the <110> rows the Cu and Au atoms alternate. **Figure 13a** presents ovals depicting the dependence of the energy

quasi-single (QS)––1 and quasi-double (QD)––2 scattering branches. Shown in the bottom panel are the corresponding angular distributions of ions scattered from <110> rows in the Au(100), Cu(100), and Cu3Au(100) planes. The dashed ovals correspond to the Au atoms, the chain one to the Cu atoms, and the solid oval with a characteristic break (3) to a row of alternating Cu and Au atoms. In the case of a mixed row, the oval has an unusual shape in that the QD branch is replaced by quasi-triple scattering (3) from a sequence of Au–Cu–Au atoms with the principal deflection from the Cu atom which results in considerable energy losses. The QS- and QD-scattering occur in this case primarily from Au atoms. The angular distribu‐ tion contains in the region, corresponding to the break in the oval, an additional maximum and exhibits a dramatic broadening. The maximum appears as a shoulder at *ψ* = 15°, grows with increasing grazing angle, and exceeds in height at *ψ* = 19° the maxima at the limiting scattering angles. As follows from the calculation, the additional maximum comes from the rainbow effect associated with the enhanced scattering close to the shadow-cone boundary of the Au atom toward the nearest Cu atom in a narrow impact parameter region along the row.

**Figure 13b** shows also the scattering ion energy versus the scattering angle ovals and the corresponding angular distributions; however, in this case, in the alternating sequence of atoms, one of them, either Au or Cu occurs twice in succession. Both the energy ovals and the angular distributions are seen to vary dramatically. It is shown when two neighboring atoms belong to the same species, the characteristic break (3) transforms into an additional oval which lies lower than the principal one and corresponds to QS- and QD-scattering from a pair of Cu atoms. To this oval correspond two additional maxima in the angular distribution. A similar pattern is also observed in the case when two Au atoms adjoin one another in a mixed row. The relative height of the additional maxima was found to depend on the number of neigh‐ boring atoms of the same species in a row. Increasing the number of neighboring identical atoms up to three or more results in an increase of the corresponding additional maxima in the angular distribution. Note that the shape of the energy oval and the interval of possible scattering angles are retained, whereas relative height of the maxima at the limiting scattering angles decrease. The characteristic structure of the angular distribution with the number of maxima is also retained when thermal vibrations of atoms in the alloy are included. Thus, a comparison of the angular and energy distributions of ions scattered from the surface of an alloy in the process of ordering with similar distributions for pure targets made up of the alloy components permits a conclusion that two or more neighboring atoms in an alternating sequence are of the same species. The results obtained can be used to study a short-range order

In this section, the grazing ion sputtering processes of Si(001), SiC(001), and Cu3Au(001)

bombardment have been studied by computer simulation [52, 53].

ions with initial energy *E* 0 = 5 keV on the scattering angle *θ*, which consist of

of scattered Ar+

382 Radiation Effects in Materials

in alloys undergoing ordering.

surfaces at 0.5–5 keV Ne+

**4.6. Ion sputtering of single-crystal surfaces**

**Figure 14.** Sputtering yield of Si(001) (a) and SiC(001) (b) versus angle of incidence at Ne+ ion bombardment.

In **Figure 14a,b** the angular dependences of the sputtering yield for Si(001) and SiC(001) surfaces subdivided into sputtering by the first three surface layers at 0.5 keV Ne+ ion bom‐ bardment are compared. Note the angle of incidence *ψ* is counted from the surface. It is seen that there is a threshold angle of sputtering in all dependences. At angles of incidence less than the threshold angle, the incident ions cannot penetrate into the crystal and cannot eject target atoms. The threshold angle shifts to the lower values of angle of incidence with increasing the energy of incident ions. At *ψ* large than a threshold angle, with increasing *ψ* the number of PKR at first rises and achieves its maximum. There is a plateau (shorter for Si and wider for SiC) near the threshold angle because of insufficient ion energy for both long moving ions within surface semichannels and their penetration to deeper layers. With increasing the initial energy, this plateau disappears, and the sputtering yield decreases at large *ψ*. This decreasing of PKR yields is explained by partial penetration of ions into deeper layers and domination of the cascade sputtering mechanism. It is clear that the relative contributions of each layer to the total PKR yield strongly depend on the angle of incidence. In the angular range of *ψ* = 11–20° for Si and 15–23° for SiC, the sputtering occurs only from the first layer.

It is seen that the threshold angle is a bit smaller in the case of Si than for SiC. As results for high initial energy show, in general the sputtering yield is large in the case of SiC. These dependences allow choosing an angle of incidence for an effective sputtering at given initial energy. In **Figure 15a,b**, the sputtering yields of Si(001) and SiC(001) surfaces subdivided into sputtering by the first three surface layers versus the energy of incident Ne+ ions are shown at *ψ* =10°. The threshold energy of sputtering is about 1 keV for these cases. There is more drastic increase of sputtering yield in the beginning of dependences for Si than for SiC. It is seen that the main contribution to the total sputtering comes from the sputtering of the first layer. Moreover, in the energy range of 0.5–1.5 keV for Si and 1–3 keV for SiC, the sputtering occurs only from the first layer. Further increasing of the ion energy results in increasing the contri‐ bution from second and third layers. The contribution to sputtering from the third layer is larger than the one from the second layer, as the atomic rows in the second layer lies directly under the one of the first layers in the <110> direction. Two local maxima at 2.5 and 4 keV are observed in the total sputtering yield dependence in the case of Si. Sputtering from the first layer gives a basic contribution to the first maximum, while the second maximum is formed by atoms ejected from the second and third layers. In the case of SiC the maximum of total dependence is formed by atoms ejected from the second layer. These results show that by choosing an angle and an energy of incidence, one can produce layer-by-layer sputtering of Si(001) and SiC(001) surfaces.

In **Figure 16**, the sputtering yield of Cu3Au(001) versus polar (*ψ*) and azimuth (*ξ*) angle of incidence at 5 keV Ne+ ion bombardment is presented. Azimuthal angular dependence is shown only for the range of *ξ* = 0–90° due to its symmetricity. The main maxima at *ξ* = 0 and *ξ* = 90°, two local maxima at *ξ* = 35° and *ξ* = 55°, and deep minimum at *ξ* = 45° are observed in low crystallographic directions and near them. They are caused by the existence of original semichannels and channels in these directions. In these directions the incident ions either penetrate deeper into crystal or undergo the surface semichanneling. Due to ion channeling, the multiple collisions of projectile with target atoms are possible resulting in an intensive surface sputtering. Besides, the sputtering yield of Cu3Au(001) is two times less than one for SiC(001). These results show that influence of crystal orientation to sputtering yield depends on both crystal structure and its composition.

**Figure 15.** Sputtering yield of Si(001) (a) and SiC(001) (b) versus energy of incident Ne+ ions at *ψ* =10°.

It is seen that the threshold angle is a bit smaller in the case of Si than for SiC. As results for high initial energy show, in general the sputtering yield is large in the case of SiC. These dependences allow choosing an angle of incidence for an effective sputtering at given initial energy. In **Figure 15a,b**, the sputtering yields of Si(001) and SiC(001) surfaces subdivided into sputtering by the first three surface layers versus the energy of incident Ne+ ions are shown at *ψ* =10°. The threshold energy of sputtering is about 1 keV for these cases. There is more drastic increase of sputtering yield in the beginning of dependences for Si than for SiC. It is seen that the main contribution to the total sputtering comes from the sputtering of the first layer. Moreover, in the energy range of 0.5–1.5 keV for Si and 1–3 keV for SiC, the sputtering occurs only from the first layer. Further increasing of the ion energy results in increasing the contri‐ bution from second and third layers. The contribution to sputtering from the third layer is larger than the one from the second layer, as the atomic rows in the second layer lies directly under the one of the first layers in the <110> direction. Two local maxima at 2.5 and 4 keV are observed in the total sputtering yield dependence in the case of Si. Sputtering from the first layer gives a basic contribution to the first maximum, while the second maximum is formed by atoms ejected from the second and third layers. In the case of SiC the maximum of total dependence is formed by atoms ejected from the second layer. These results show that by choosing an angle and an energy of incidence, one can produce layer-by-layer sputtering of

In **Figure 16**, the sputtering yield of Cu3Au(001) versus polar (*ψ*) and azimuth (*ξ*) angle of

shown only for the range of *ξ* = 0–90° due to its symmetricity. The main maxima at *ξ* = 0 and *ξ* = 90°, two local maxima at *ξ* = 35° and *ξ* = 55°, and deep minimum at *ξ* = 45° are observed in low crystallographic directions and near them. They are caused by the existence of original semichannels and channels in these directions. In these directions the incident ions either penetrate deeper into crystal or undergo the surface semichanneling. Due to ion channeling, the multiple collisions of projectile with target atoms are possible resulting in an intensive surface sputtering. Besides, the sputtering yield of Cu3Au(001) is two times less than one for SiC(001). These results show that influence of crystal orientation to sputtering yield depends

ion bombardment is presented. Azimuthal angular dependence is

Si(001) and SiC(001) surfaces.

on both crystal structure and its composition.

incidence at 5 keV Ne+

384 Radiation Effects in Materials

**Figure 16.** Sputtering yield of Cu3Au(001) versus polar (a) and azimuth (b) angle of incidence at *E*0 = 5 keV.

Thus, the peculiarities of formation of PKR atoms at grazing ion incidence beam on an atomically smooth surface of a single crystal promotes its layer-by-layer sputtering. For the realization of the layer-by-layer sputtering mechanism, it is nessesary that a part of the ion energy, corresponding to the normal components of its velocity, will be lower than a threshold of sputtering of atoms of a layer, next to the surface one, that is, *E <sup>i</sup>* sin2 *ψ <sup>i</sup>* < *E <sup>d</sup>*, where *E <sup>i</sup>* is the ion energy before the *i*th collision, *ψ <sup>i</sup>* is the angle between the ion movement direction and the semichannel axis before the *i*th collision, and *E <sup>d</sup>* is the energy of displacement of atoms of a second layer (in the case considered, the bottom chain of semichannel). In these conditions it is possible to achieve successive removal of layers without disturbance of the next layer at removal of the previous one. Ion bombardment at grazing angles reduces considerably the influence of effect of crater walls and ion mixing on the results of layer-by-layer analysis, and increases its accuracy and sensitivity.

Parameters of single crystals (lattice parameter, binding energy, and mass of atoms) influence significantly the angular and energy dependences of sputtering yield. In general, the sputter‐ ing yield of the SiC(001) surface is larger than the one of the Si(001) surface. The proposed mechanism of layer-by-layer sputtering of a single-crystal surface at ion bombardment under grazing angles needs detailed checking and investigation by computer simulation as well as on experimental basis.

#### **4.7. Determination of adatom sort and adsorption sites on single-crystal surfaces by ions channeling through thin films**

Determination of the equilibrium adsorption sites of atoms adsorbed on crystalline surfaces and initial stages of adsorption is a fundamental problem in surface physics. Stensgaard [54] was the first to propose for the determination of the adsorbed site of D atoms adsorbed on the rear (100) surface of a thin Ni single crystal, 800 keV He+ ions which channel through the sample. The adatoms were detected by monitoring the yield of the D( 3 He,p) 4 He reaction. In the present section, we propose for the determination of the adsorption site and sort of light adatoms on the rear surface of a thin crystal to use interaction with these adatoms of low energy ions of mass *m* <sup>1</sup> greater than the adatom mass *m* 2, channeling through the crystal. For *m* 1 > *m* 2, there exist a limiting angle *θ* lim = arcsin(*μ*), where *μ* = *m* 2/*m* 1, which leads to the rainbow effect in scattering, that is, enhanced reflection that results in the appearance in the angular and energy distributions of transmitted ions of characteristic peaks useful for diagnostics purposes. In order to improve the usefulness of the angular and energy distributions of transmitted particles for diagnostic purposes, it can be recommended to also employ, besides the rainbow effect, the flux peaking phenomenon, that is, a spatial redistribution of the channeling particles in the transverse channel plane, which produces an increase of the flux in the central part of the channel and its sharp decrease on its periphery [56]. The sort and adsorption site of the adatoms are determined from the rainbow effect in the angular distri‐ butions of transmitted particles caused by their interaction with adatoms above the rear surface of the crystal [55, 56].

**Figure 17.** (a) The possibility of using the channeling effect to detect the adatom adsorption site above the rear crystal surface along the principal axes. (b) The changes in the angular distribution of the redistributed transmitted flux caused by the ion interaction with the adatom.

The trajectories of 1–5 keV He+ and Ne+ ions channeling in thin (Δ*z* = 100–500 Å) Ni(100) films were computer-simulated in the binary collision approximation using the universal Biersack– Ziegler–Littmark potential and with the inclusion of elastic and inelastic energy losses. For ions emerging out of the rear side of the crystal, one calculates the coordinates of the emergence points projected on a plane perpendicular to the channel axis, the total scattering angle (the angle between the initial and final ion directions), and the final ion energy. Next, one calculates the interaction of the transmitted ions with the adsorbed atoms residing in various positions relative to the channel axis and at given heights *h* with respect to the rear surface of the crystal. The adatom sort and adsorption site are determined from a comparison of the angular distributions of the transmitted ions with or without adatoms present on the crystal surface (Figure 17a,b). **Figure 17a** illustrates the possibility of using the channeling effect to detect the adatom adsorption site above the rear crystal surface along the principal axes. **Figure 17b** shows schematically the changes in the angular distribution of the redistributed transmitted flux caused by the ion interaction with the adatoms. We readily see that the presence of a peak in the angular distribution at the limiting scattering angle permits the identification of the adatom sort. Thus, the present method is efficient only when m2 < m1, that is, when the adatoms are lighter than the channeling ions. By choosing properly the ion energy and crystal thickness, one can obtain angular distributions with the main peak corresponding to the limiting scattering angle.

adatoms on the rear surface of a thin crystal to use interaction with these adatoms of low energy ions of mass *m* <sup>1</sup> greater than the adatom mass *m* 2, channeling through the crystal. For *m* 1 > *m* 2, there exist a limiting angle *θ* lim = arcsin(*μ*), where *μ* = *m* 2/*m* 1, which leads to the rainbow effect in scattering, that is, enhanced reflection that results in the appearance in the angular and energy distributions of transmitted ions of characteristic peaks useful for diagnostics purposes. In order to improve the usefulness of the angular and energy distributions of transmitted particles for diagnostic purposes, it can be recommended to also employ, besides the rainbow effect, the flux peaking phenomenon, that is, a spatial redistribution of the channeling particles in the transverse channel plane, which produces an increase of the flux in the central part of the channel and its sharp decrease on its periphery [56]. The sort and adsorption site of the adatoms are determined from the rainbow effect in the angular distri‐ butions of transmitted particles caused by their interaction with adatoms above the rear surface

**Figure 17.** (a) The possibility of using the channeling effect to detect the adatom adsorption site above the rear crystal surface along the principal axes. (b) The changes in the angular distribution of the redistributed transmitted flux

were computer-simulated in the binary collision approximation using the universal Biersack– Ziegler–Littmark potential and with the inclusion of elastic and inelastic energy losses. For ions emerging out of the rear side of the crystal, one calculates the coordinates of the emergence points projected on a plane perpendicular to the channel axis, the total scattering angle (the angle between the initial and final ion directions), and the final ion energy. Next, one calculates the interaction of the transmitted ions with the adsorbed atoms residing in various positions relative to the channel axis and at given heights *h* with respect to the rear surface of the crystal. The adatom sort and adsorption site are determined from a comparison of the angular distributions of the transmitted ions with or without adatoms present on the crystal surface (Figure 17a,b). **Figure 17a** illustrates the possibility of using the channeling effect to detect the adatom adsorption site above the rear crystal surface along the principal axes. **Figure 17b**

and Ne+ ions channeling in thin (Δ*z* = 100–500 Å) Ni(100) films

of the crystal [55, 56].

386 Radiation Effects in Materials

caused by the ion interaction with the adatom.

The trajectories of 1–5 keV He+

This is illustrated in **Figure 18**, showing angular distributions of 1 keV Ne+ ions channeling through thin (Δ*z* = 100 Å) Ni(100) films along <100> in the (a) absence and (b) presence of adatoms of carbon and (c) oxygen located at the channel center at a height *h* = 0.9 Å above the rear crystal surface, which were calculated for *T* = 0 K. The presence of adatoms affects noticeably the distributions in that they shift toward scattering angles *θ* ≈ *θ* lim, their main peaks corresponding to rainbow scattering (*θ* lim = 35° for carbon and *θ* lim = 50° for oxygen). The essential advantage of this method lies in its capability of detecting of very light adatoms, such as hydrogen and deuterium. Thickness of the film, channeling direction, and particle energy have influence only on the magnitude of these maxima, but not on their positions. Thus, this method allows discrimination between the isotopes of an adsorbed element. Similar argu‐ ments are valid also for close isotopes of carbon and oxygen. Thus, when *m* 1 > *m* 2, the angular distributions of transmitted ions allow a correct determination of the adatom sort. The film thickness is not a critical factor in this technique, and it can be taken thicker if one increases correspondingly the initial energy of ions.

**Figure 18.** Angular distributions of 1 keV Ne+ ions channeling through thin Ni(100) films in (a) absence and (b) pres‐ ence of adatoms of carbon and (c) oxygen.

It is thought that rapid progress of the nanostructures physics and ultra-high vacuum technology allow to obtain in near future single-crystal films only a few hundred Angstroms thick with clean entrance and exit surfaces and well-ordered adsorbate structure on them. It was shown that the magnitude of main maximum at *θ* ≈ *θ* lim depends on the height *h* of the adatom above the crystal surface. For the case Ne+ → Ni(100) + O, where film thickness (Δ*z* = 100 Å) and *E* <sup>0</sup> = 1 keV, maximum occurs at *h* = 0.9 Å, which is in agreement with the experi‐ mental value [57]. The sensitivity of the angular distributions of transmitted ions to shadowed adatom positions which do not correspond to the channel center in the given direction can be revealed by varying the direction of particle channeling. The accuracy with which the adatom adsorption site with respect to the unit cell in the transverse plane of the channel can be determined is evaluated as ~0.1 Å. An experimental test of this technique would permit a realistic evaluation of its capabilities.
