**4. Discussion**

For the generation of aligned nanogrooves, we did not use a convergent nanosized electron beam as has been done for the generation of nanoholes [10] but a homogeneous electron beam of about 200–800 nm in diameter. In this case, the phenomena occurring on the electron exit surface may be as follows (Figure 18). Surface vacancies are formed at first in the first layer of the metal. Then, the surface vacancies agglomerate to produce monolayer islands of surface vacancies. Under prolonged irradiation, surface vacancies are produced in the area of islands, and multilayered pits are formed in several minutes. One cannot expect any anisotropic movement of surface vacancies on (001) and (111) surfaces in the process, but it may be expected on (011), judging from the nature of geometrical symmetry of the surfaces. Therefore, the present results on the pattern formation on the

(001) surface strongly suggest that we are dealing with a case of self-organized pattern formation controlled by some factor, which includes the anisotropy of material transfer. rical symmetry of the surfaces. Therefore, the present results on the pattern formation on the (001) surface strongly suggest that we are dealing with a case of self-organized pattern formation controlled by some factor, which includes the anisotropy of material transfer.

exit surface of Fe where the pattern developed should be rather clean due to sputtering.

For the generation of aligned nanogrooves, we did not use a convergent nanosized electron beam as has been done for the generation of nanoholes [10] but a homogeneous electron beam of about 200–800 nm in diameter. In this case, the phenomena occurring on the electron exit surface may be as follows (Figure 18). Surface vacancies are formed at first in the first layer of the metal. Then, the surface vacancies agglomerate to produce monolayer islands of surface vacancies. Under prolonged irradiation, surface vacancies are produced in the area of islands, and multilayered pits are formed in several minutes. One cannot expect any anisotropic movement of surface vacancies on (001) and (111) surfaces in the process, but it may be expected on (011), judging from the nature of geomet-

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 14 of 20

Further investigations on this point are desired.

**4. Discussion** 

**Figure 18.** A sketch of the change in the electron exit surface at the initial stage of formation of pits. 1. At first, vacancies are formed on the surface layer of the foil by sputtering. 2. They then agglomerate to form monolayer islands of surface vacancies. 3. After prolonged irradiation, further surface vacancies are formed within islands. 4. Finally, multilayered pits will be formed. **Figure 18.** A sketch of the change in the electron exit surface at the initial stage of formation of pits. 1. At first, vacancies are formed on the surface layer of the foil by sputtering. 2. They then agglomerate to form monolayer islands of surface vacancies. 3. After prolonged irradiation, further surface vacancies are formed within islands. 4. Finally, multilayered pits will be formed.

We have found the formation of pits and the self-organization of grooves under electron irradiation. The growth process of the pits has been discussed theoretically by Cherns [11]. However, his model does not predict the generation of the deep nanoholes and the aligned nanogrooves found in the present work; probably, he used Au(111) foils on which the aligned nanogrooves do not appear. It is not clear when and why the aligned nanogrooves and the deep nanoholes are generated. In this section, we discuss the formation of deep nanoholes and the self-organization process of nanogrooves. We have found the formation of pits and the self-organization of grooves under electron irradiation. The growth process of the pits has been discussed theoretically by Cherns [11]. However, his model does not predict the generation of the deep nanoholes and the aligned nanogrooves found in the present work; probably, he used Au(111) foils on which the aligned nanogrooves do not appear. It is not clear when and why the aligned nanogrooves and the deep nanoholes are generated. In this section, we discuss the formation of deep nanoholes and the self-organization process of nanogrooves.
