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Chain effect for the inverse mass ratio of colliding particles in grazing ion–surface interactions
Chain effect for the inverse mass ratio of colliding particles in grazing ion–surface interactions A.A. Dzhurakhalov a,*, F.F. Umarov b a Institute of Electronics, F.Chodjaev Str. 33, 700143 Tashkent, Uzbekistan b Institute of Applied Physics of the Tashkent State University, 700095 Tashkent, Uzbekistan
Abstract A computer simulation was used to study, in the binary collision approximation, the trajectories, energy and angular distributions of 5–15-keV Kr+, Xe+ and Rn+ ions scattered from atomic chain ridges on Cu(100) and V(100) surfaces in the 110 direction with a grazing angle interval 5–25°. It was observed that for the inverse mass ratio of collision partners, i.e. when the incident ion is heavier than target atom, the atomic chain effect manifests itself in a number of features associated with the existence of a limiting scattering angle in a single collision. It has been shown that a specific feature of the atomic row effect for the inverse mass ratio of colliding particles results in the appearance of characteristic peaks in the angular and energy distributions useful for diagnostic purposes. © 1998 Elsevier Science S.A. Keywords: Atomic chain effect; Ion scattering
1. Introduction When investigating of small angle ion scattering from a single crystal surface, the atomic chain effect is usually observed. This effect consists of the existence of a double-valued pattern of the dependence of particle energy on scattering angle and the confinement of the scattered beam between a maximum and a minimum escape angle [1,2]. In experimental studies of small angle ion scattering from the surface of crystals, a situation may arise where a target atom may be lighter than the projectile. It would thus be of interest to investigate the atomic chain effect for the inverse mass ratio of collision partners, i.e. where the mass of the ion m is greater than that of the 1 atom in the chain m , so that m=m /m <1. The atomic 2 2 1 chain effect manifests itself in this case in a number of features associated with the existence of a limiting scattering angle h =arcsin m in a single collision, as lim well as with the fact that the scattering at a given angle h
(the diagram representing the scattered ion energy versus the scattering angle) from an atomic chain for m >m 1 2 is observed, unlike those observed for m
2. Theoretical background and simulation techniques 2.1. Influence of inelastic energy losses on the kinematics of elementary ion–target atom collision The expressions for the ion (E ) and target atom 1 (E ) (recoil ) energies, taking into account inelastic losses 2 e(E ,P) can be written in the form: o E =(1+m)−2E (cos h ±E(mf )2−sin2 h )2, 1 o 1 1 E (1) E =m(1+m)−2E (cos h ± f 2−sin2 h )2, 2 2 o 2 where E is the ion energy before collision, P is the o impact parameter, f={1−(1+m)/m [e(E ,p)/E ]}1/2<1 is o o the inelastic energy loss factor ( f=1 in the case of
A.A. Dzhurakhalov, F.F. Umarov / Surface and Coatings Technology 103–104 (1998) 16–19
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elastic scattering), and h and h are the scattering angles 1 2 of the ion and recoil atom, respectively. The relations between the angles h , h and the scatter1 2 ing angle x in the centre-of-mass system in this case take the form:
by the nature of the particles and by the magnitude of the inelastic energy losses.
tan h =sin x/( mf )−1+cos x, 1 tan h =sin x/f −1−cos x. 2
Trajectories of the incident ions experiencing correlated sliding scattering on the discrete atomic chains along the 110 direction on the Cu(100) and V(100) surface have been simulated in the binary collision approximation with regard to the time integral. Particle interactions were described by the universal Biersack–Ziegler–Littmark potential [7]. Elastic and inelastic energy losses of scattered ions have been summed along their trajectories. The inelastic energy losses have been calculated on the basis of the modified Firsov model [8] and included in the scattering kinematics. Thermal vibrations of target atoms were not considered. The evaluations showed that the inclusion of the random thermal vibrations at T=300 K does not significantly reduce the observed effects and results primarily in a certain decrease of the peaks on energy and angular distributions of the scattered particles. For consideration of possible simultaneous or nearly simultaneous collisions of ion with several target atoms, the procedure proposed by Robinson and Torrens [9] was used. Details of the calculations have been described in Ref. [8].
(2)
From Eq. (2), for a given impact parameter, the scattering, h , and recoil, h , angles are smaller than in 1 2 the elastic process [6 ], which means that inelastic collisions result in a change of the ion and recoil directions of motion. This leads to an interesting consequence associated with the fact that all specific features of an elementary collision event originating from the inverse mass ratio of the colliding particles will also be observed in the practically essential case of m=1 (e.g. for collisions of crystal atoms with one another), and even for m slightly in excess of unity. The inclusion of inelastic energy losses results for m<1 in a reduction of the value of h compared with that calculated for the elastic lim process. In this case: h ≤h =arcsin ( fm). (3) 1 1lim From Eq. (3), there may exist h for m=1 as well as lim for m slightly greater than unity, provided that fm<1. Another essential consequence of the inclusion of inelastic energy losses is the existence (irrespective of the value of m) of a limiting angle h for the recoil atom: 2 h ≤h =arcsin ( f ). (4) 2 2lim Fig. 1 shows schematically the dependencies of the angles h and h on the impact parameter, P, for the 1 2 case m=1 with inclusion (full curves) and without inclusion (dashed curves) of inelastic energy losses. When the inelastic energy losses are included, the angles h and 1 h reach maximum values lower than 90° for certain P 2 values, with h +h ≠90°. In head-on collisions (P=0), 1 2 h =0 rather than 90°, as in the case of the elastic 1 collision. The quantities h and h are determined 1lim 2lim
Fig. 1. Scattering angles for the ion, h , and the recoil atom, h , versus 1 2 the impact parameter P for the case m=1 with (full curves) and without (dashed curves) inelastic energy losses.
2.2. Computer simulation techniques
3. Results and discussion Fig. 2 shows the dependence of the energy, E, retained by the Kr+ ions scattered from copper atomic rows, on the scattering angle h, for grazing angles y=17.5 and 22.5°. On the right-hand side of Fig. 2, the usual behaviour of h(P) for m<1 is shown. In this case, m=0.758, h =49°, E=2096 eV, e=54 eV and P =0.008 nm. lim lim
Fig. 2. Dependencies of the ion energy, E, on the scattering angle, h, for 15 keV Kr+ ions scattered from 110 atomic rows on Cu(100) surface, for grazing angles y=17.5° and 22.5°. Top, the various scattering schemes. Right, schematic of the h(P) dependence.
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For m<1, the scattered ion energy determined by Eq. (1) is a double-valued function of the scattering angle: the plus sign corresponds to the larger (P>P ), and the lim minus sign to the smaller (P
1. Indeed, for y=17.5°, one observes a double-valued dependence E(h) caused by the conventional quasisingle (QS) (branch 2) and quasidouble (QD) (branch 3) scattering, as well as blocking on the sides of small and large scattering angles. Notice that at a small y value, the scattering angles in the case of an atomic row are smaller than h for a single collision, lim the ions do not approach the atoms in the row close enough, and the impact parameters P are greater than i P . lim As the grazing angle increases (y=22.5°), small impact parameters P
10°, the region of possible scattering angles grows with increasing y, and the atomic row effect results in the possibility of scattering at angles greater than h up to a factor of lim three, with Rn+ ions colliding at y=20°. Interestingly, not only the maximum, but also the minimum, escape angles in this case exceed the specular angle, so that the scattering becomes supraspecular. For still increasing
Fig. 3. (a) Dependencies of the ion energy, E, on the scattering angle, h, for 15 keV Kr+ (1), Xe+ (2) and Rn+ (3) ions scattered from 110 atomic rows on Cu(100) surface for y=20°. (b) Maximum and minimum values of the escape angle, d versus grazing angle, y, for Kr+ (dots), Xe+ (dash–dot) and Rn+ (full curves) ions.
y values, the collisions become essentially multiple (whereas for a direct mass ratio, the number of collisions conversely decreases), with a fraction of the ions penetrating through the atomic row, just as in the m>1 case. Fig. 4 shows the dependencies of the energy, E, retained by the 8.22 keV Kr+ ions scattered from atomic rows in the 110 direction on the V(100) surface, on the scattering angle h, for various y values. The position of h #h is not sensitive to the change of grazing angle I lim y. When y increases, the position of h is shifted to the II region of large scattering angles.
Fig. 4. Dependencies of the ion energy, E, on the scattering angle, h, for 8.22 keV Kr+ ions scattered from 110 atomic rows on V(100) surface, for several values of grazing angle, y.
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observed in the simulations, when an inverse mass ratio holds between colliding particles, result in complicated angular and energy distributions of scattered ions, which present an interesting experimental problem.
4. Conclusions
Fig. 5. Dependence of the ion energy, E, on the scattering angle, h, for 15 keV Kr+ ions scattered from 110 atomic rows on Cu(100) surface, for y=20 (top panel ) and the corresponding angular distribution (bottom panel ).
The processes occurring when 5–15-keV Kr+, Xe+ and Rn+ ions are scattered from atomic chain ridges on Cu(100) and V(100) surfaces in the 110 direction have been investigated by computer simulations at various grazing angles. It was observed that, for the inverse mass ratio of collision partners, the atomic chain effect manifests itself in a number of features associated with the existence of a limiting scattering angle in a single collision event. A specific feature of the atomic row effect for the inverse mass ratio of colliding particles is the appearance of characteristic peaks in the angular and energy distributions caused by the rainbow effect, which may be useful for diagnostic purposes.
References The existence of a limiting scattering angle for m<1 leads to the rainbow effect in scattering, i.e. to the enhanced reflection, which is the origin of characteristic peaks in the angular and energy distributions, useful for diagnostic purposes (m =m sin h ). 2 1 1lim The lower panel of Fig. 5 shows the angular distribution of 15-keV Kr+ ions scattered from a copper atom row at a grazing angle y=20°. In contrast to the case of a direct mass ratio, one observes here additional maxima caused by the rainbow effect in QS, QD and multiple scattering. Taking into consideration the thermal vibrations of the atomic row results in a blurring of the peaks rather than their merging since the separations between them are fairly large. Thus, the specific features of the atomic row effect
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