UDC 537.534.8

PHYSICS

Academician of the Academy of Sciences of the Uzbek SSR U. A. ARIFOV, A. A. ALIEV

THE INFLUENCE OF THERMAL VIBRATIONS OF LATTICE ATOMS ON THE ANGULAR AND ENERGY DISTRIBUTION OF IONS SCATTERED BY A SINGLE CRYSTAL

We have investigated ((^1,\,^2)) the influence of the crystalline structure on the angular and energy distributions of ions scattered by a single crystal in the region of low ion energies (less than 5000 eV). It was shown that the relative intensity of the double-scattering peak* increases with increasing atomic numbers of the ion (z_1) and the target atom (z_2), and decreases with increasing energy of the primary ions (E_0), scattering angle (\beta), and distance (L) between the atoms on which successive scattering occurs. It was observed that the maximum energy of ions scattered along a close-packed chain is greater than in the case of a less densely packed chain. It was established that the peaks of multiple (double) collisions are more clearly expressed when the principal scattering atoms are atoms of the more close-packed directions of the crystal. It was shown that in the region (E_0 < 200) eV the influence of the binding energy of the target atoms on ion scattering differs along different crystallographic directions.

Experimental studies of the angular regularities of the interaction of ions with a single crystal make it possible to obtain quantitative information necessary for constructing a theory of ion scattering by a solid. In this respect, especially valuable are the data that can be obtained in studying the influence of thermal vibrations of the target-lattice atoms on the angular and energy distributions of ions scattered by a single crystal.

In the region of intermediate ion energies (10–30 keV), such a study was carried out in two works ((^5,\,^6)). The faces of Ni and Cu single crystals were bombarded with Ar(^+) ions. In ((^6)), special attention was paid to the influence of the target temperature on the angular distributions, the width of the energy spectra, and the course of the dependence of the intensity ratio of the peaks of singly and doubly scattered Ar(^+) ions on the initial energy of the bombarding ions. It was found that the influence of the target temperature on the scattering process is considerably greater when both the glancing angle and the scattering angle are small.

It was of interest to carry out analogous studies in the region of low ion energies ((E_0 < 5000\ \text{eV})), using single-crystal targets made of refractory metals such as W and Mo, which makes it possible to vary the temperature over wider limits (300–3000° K). The present work is devoted to investigating the influence of the crystalline structure on the angular and energy distribution of secondary ions at different target temperatures.

The study was carried out on an apparatus described in ((^7)), in which provision was made for ion bombardment of the target at different angles of incidence (\Phi) by means of a movable ion source. Energy analysis of secondary ions emitted at different angles of emergence (\theta) and scattering (\beta) was performed by means of a special device that allowed the orientation of the target to be changed. The experimental setup made it possible to investigate the change in the angular and energy

* It is known that in the energy distributions of ions scattered by a single crystal, along with peaks corresponding to an ion singly scattered by a recoil atom, there are also peaks corresponding to ions that have undergone multiple scattering on target atoms ((^3,\,^4)).

distribution of secondary ions as a function of the azimuthal angle of rotation of the target (\varphi). The angles (\Phi), (\theta), (\beta), and (\varphi) in the apparatus were changed from outside by means of magnets, which made it possible to follow changes in the character of the angular and energy distributions of the ions under the same conditions of target-surface temperature ((T = 300\text{--}2000^\circ\mathrm{K})) and vacuum ((1 \div 2)\cdot 10^{-7}) torr.

A cylindrical Hughes–Rojansky condenser served as the energy analyzer of the secondary ions, with a resolving power (\Delta E/E \approx 0.7\%). To amplify the current at the analyzer output, an ion–electron multiplier with a gain factor of (\sim 10^8) was used.

Fig. 1. Oscillograms of the energy distribution of secondary ions obtained under bombardment of the (100) face of Mo by Rb(^+) ions with energy (E_0 = 1000) eV. (1 — T_1 = 1000^\circ\mathrm{K}), (2 — T_2 = 2000^\circ\mathrm{K}), (\Phi = \theta = 75^\circ).

Figure 1 shows two oscillograms of the energy distributions of secondary ions obtained by bombarding the (100) face of a Mo single crystal with Rb(^+) ions of energy (E_0 = 1000) eV. The orientation of the target here was such that the incident and scattered beams lay in the plane of incidence passing through the ([100]) axis of the target. The angles (\Phi) and (\theta) were equal to one another and close to the glancing angles ((\Phi = \theta = 75^\circ)). Oscillogram 1 (Fig. 1) was obtained at a target temperature (T_1 = 1000^\circ\mathrm{K}), and oscillogram 2 at (T_2 = 2000^\circ\mathrm{K}).

Measurements of the energy positions of the peaks and comparison of them with calculated values obtained on the basis of a simple two-atom model of the scattering process show that here, as also in works ((^3,{}^8)), the peak with index ([000]) on oscillogram 2 corresponds to ions that have undergone single collisions, while the peaks with indices ([010]) and ([031]) correspond to ions twice scattered by the corresponding atoms. In the case of oscillogram 1 these peaks are somewhat shifted toward higher energies. As is seen from the oscillograms, with increasing target temperature the height of the peaks decreases, while their half-width increases.

A small but reproducible shift of the spectral peaks (the shifts of the peaks were observed on the oscilloscope screen dynamically, which excluded the possibility of error in measuring their energy positions at different target temperatures) toward higher energies with decreasing target temperature apparently indicates the presence of ions scattered by a chain of atoms of the crystal. Indeed, machine calculations ((^9)) showed that, when ions are scattered by a chain of atoms of the crystal, two peaks may be observed, but both are due to collisions of higher multiplicity than single and double ones. Assuming that the peaks in the case of oscillogram 1 (Fig. 1) are due to collisions of higher multiplicity, their shift toward lower energies with increasing temperature

of the target is understandable. An increase in the amplitude of thermal vibrations of the lattice atoms leads to a change in the conditions of mutual shielding of atoms in the chain on which scattering of the fast ion occurs, and this in turn leads to an increase in the probability of single and double collisions of the ion with the target atoms as compared with collisions with the chain (^{(10)}). Therefore, in the case of oscillogram 2 the peaks are true peaks of single and double collisions and, accordingly, are shifted toward lower energies in comparison with the peaks of chain collisions.

Fig. 2. Dependences of (\eta_{[000]T_1}) ((a)), (\eta_{[010]T_1}) ((b)), (\eta_{[000]T_2}) ((v)), and (\eta_{[010]T_2}) ((g)) on the scattering angle (\beta). (a') and (b') are theoretical (\eta_{[000]}), (\eta_{[010]}).

Figure 2 gives the dependences (\eta_{[000]T_1}), (\eta_{[010]T_1}), (\eta_{[000]T_2}), (\eta_{[010]T_2}) on the scattering angle (\beta). Here (\eta_{[000]}) and (\eta_{[010]}) are the ratios of the energies of secondary ions that have undergone single and double collisions to the energy of the primary ions (E_0). For comparison, the dependences of the theoretical values (\eta_{[000]T}) and (\eta_{[010]T}) on (\beta) are plotted there as well (dashed curves). It is seen that the curves (\eta_{[000]T_2}(\beta)) and (\eta_{[010]T_2}(\beta)) deviate from the analogous curves for low temperatures in the region of scattering angles (\beta \leq 30^\circ). This shows that the influence of thermal vibrations of the lattice atoms is greater for ions incident on the target at glancing angles.

Figure 3 gives the dependence (R = I_2/I_1)—the ratio of the intensity (height) of the double peak (I_2) to the intensity of the single peak (I_1), in arbitrary scale, on the azimuthal angle of rotation of the target (\varphi). Here diagram 1 (Fig. 3) refers to the oscillogram of the energy distribution of secondary ions obtained upon bombardment of the (100) face of a molybdenum target heated to (T_1 = 1000^\circ)K, and diagram 2 to the same target at (T_2 = 2000^\circ)K. It is seen that, depending on the target temperature, the value (R(\varphi)) changes; the temperature effect is stronger along more densely packed directions than along less densely packed ones. This apparently indicates anisotropy of the vibration amplitude of the lattice atoms along different crystallographic directions, which should lead to a smoothing of the differences in the packing of atoms in chains and thereby to a smoothing of the anisotropy of the value of (R) as a function of the azimuthal angle of rotation of the target (^{(1)}).

Fig. 3. Dependence of the intensity (height) of the double peak [010] on the azimuthal angle (\varphi) of rotation of the target, in arbitrary units. (\mathrm{Rb}^+) on Mo (100), (\Phi = \theta = 70^\circ).
1 — (T_1 = 1000^\circ)K, 2 — (T_2 = 2000^\circ)K.

Figure 4 gives the dependences of the coefficients of scattered (k_p), diffused (k_d), and evaporated ions (k_i) on the angle (\Phi), obtained-

... obtained in bombardment of the (100) face of a molybdenum target (heated to (T=1500^\circ\mathrm{K})) by (\mathrm{Rb}^+) ions with energy (E_0=1000) eV. For comparison, the same figure gives the dependence of the ion-scattering coefficient (k_p), obtained in bombardment of a clean cold (100) face of a molybdenum target (black points). The coefficients (k_p), (k_{\mathrm{d}}), and (k_{\mathrm{i}}) were found from the current–voltage characteristic obtained by the double-modulation method ((^{11})), which makes it possible to separate the current of scattered ions (I_p) from the diffusion current (I_{\mathrm{d}}), and the current of evaporated ions (I_{\mathrm{i}}) from the scattered current.

Fig. 4. Dependences of the scattering coefficients (k_p), diffusion (k_{\mathrm{d}}), and evaporation (k_{\mathrm{i}}) of ions on the angle of incidence of the primary ions (\Phi). (\mathrm{Rb}^+) on Mo (100)

It is seen that the anisotropy of the value of the ion-scattering coefficient (k_p) as a function of (\Phi), which we found in ((^{3})), is observed here as well. However, no noticeable change (smoothing) of the anisotropy of this coefficient as a function of the target temperature was observed here. This is apparently connected with the fact that the target temperature ((T=1500^\circ\mathrm{K})) is still insufficient for the amplitude of the thermal vibrations of the lattice atoms to appreciably affect the transparency of the crystal. To obtain a noticeable smoothing of the anisotropy of the value of (k_p), the target must apparently be brought to a temperature close to the melting temperature of the metal ((^{10})). In this case, however, the presence of thermoelectron emission will make measurement of the coefficient difficult.

As is seen from Fig. 4, along with the anisotropy of (k_p), an anisotropy of the coefficient of diffusion ions (k_{\mathrm{d}}) is also observed. This anisotropy is observed in the same directions as the anisotropy of (k_p); however, the maximum value of (k_{\mathrm{d}}) coincides with the minimum of (k_p), and conversely. The latter is explained by the channeling effect of the incident particles in the crystal lattice and their subsequent reverse diffusion to the surface of the heated target. Thus, consideration of the change in the angular and energy distribution of ions as a function of target temperature shows that these changes are due mainly to the influence of thermal vibrations of the lattice atoms on the processes of ion scattering.

The results of our investigation confirm the possibility of using ion scattering (reflection) to study the structure of a solid and the correlation of vibrations of atoms forming chains.

Institute of Electronics
Academy of Sciences of the Uzbek SSR
Tashkent

Received
17 XII 1969

REFERENCES

1. U. A. Arifov, A. A. Aliev, Proc. IX Intern. Conf. on Phenomena in Ionized Gases, Bucharest, 1969.
2. У. А. Арифов, А. А. Алиев, ЖЭТФ, 57, issue 4, No. 12 (1969).
3. А. А. Алиев, У. А. Арифов, ДАН, 172, No. 1, 65 (1967).
4. E. S. Maschkova, V. A. Molchnov et al., Phys. Lett., 18, 7 (1965).
5. E. S. Maschkova, V. A. Molchnov, V. Soshka, Phys. Stat. Sol., 19, 425 (1967).
6. В. М. Чичеров, ЖЭТФ, 55, issue 1, No. 7, 25 (1968).
7. У. А. Арифов, А. А. Алиев, А. Х. Аюханов, Изв. АН УзССР, ser. phys.-mat. sciences, No. 4, 20 (1964).
8. U. A. Arifov, A. A. Aliev, Proc. VIII Intern. Conf. on Phenomena in Ionized Gases, Vienna, 1967.
9. В. М. Кивилис, Э. С. Парилис, Н. Ю. Тураев, ДАН, 173, 805 (1967).
10. E. S. Parilis, N. Yu. Turaev, V. M. Kivilis, Proc. VIII Intern. Conf. on Phenomena in Ionized Gases, Vienna, 1967.
11. У. А. Арифов, А. Х. Аюханов, Изв. АН СССР, ser. phys., 20, 1165 (1956).