*4.2. Self-Organization of Nanogrooves*

Interesting discovery on the development of nanostructure under electron irradiation in the present study is the pattern formation of nano-grooves, which can change depending on the irradiation directions, the irradiation temperatures, and the kinds of metals. The most outstanding feature appears for Au. The nanogrooves exhibit strong irradiationdirection dependencies in their growth. They grow along [100] and [010] directions for [001] irradiation and along [100] for [011] irradiation, whereas no clear grooves are formed for [111] irradiation. The widths of nanogrooves and holes are between about 1 and 2 nm, which are the smallest ones formed on metal surfaces so far. The formation of the groove pattern also has a surface orientation dependence.

To clarify the formation mechanism on the nanostructures, systematic investigations are needed. After finding the pattern formation for Au, we investigated several FCC metals of Au, Ag, Cu, Ni, and a BCC metal of Fe. For Ag and Cu, the pattern formation is not so clear. For Ni, the diffusion effect is not so high compared to the cases of Ag and Cu, but the pattern depended on the part of the specimen, as seen in Figure 11. For Fe, the pattern is not clear but rather random (Figure 14).

The generation of nanoholes and nanogrooves originally comes from the sputtering at the electron exit surface. Thus, the anisotropic growth of the nanogrooves and nanoholes should be attributed to the irradiation-induced anisotropic flow of point defects [29].

The fact that different groove patterns observed on the same Au(001) surface by irradiating along different directions (Figures 4 and 5) strongly suggests that the patterns are meta-stable structures, which has a very long lifetime at low temperatures.

The available experimental evidence demonstrates that we are dealing with a case of self-organized pattern formation, which satisfies the following conditions.


Below 240 K, the temperature effect of surface vacancy, which will reduce the anisotropic growth of nanogrooves due to their random movements, should be low for Au, as seen in Figure 10. At the low temperature region, the migration of surface vacancies by thermal activation alone should be negligibly small. Thus, we may expect the phenomena observed to be controlled by some anisotropic mechanisms such as sputtering induced by the anisotropy of the sputtering yield [23], the surface reconstruction under irradiation [25], focused collision chains [30], or irradiation-induced diffusion [29].

We guess that the anisotropy of momentum transfer, either directly from the electrons by Rutherford scattering or indirectly through bulk collision sequences propagating along the densely packed directions, leads to the mobility of surface vacancies, finally leading to anisotropic groove patterns. One should note that there exists a difference in the anisotropy of collision sequence propagation between bulk Au and Ag, i.e., along the <100> direction for Au but <110> for Ag, which was experimentally supported by a difference in the anisotropy of the threshold energy for atom displacement in both materials [30].

Now, we draw a conceivable scenario, in the following section. Consider a surface atom of which momentum has been transferred either directly from the electrons by Rutherford scattering or indirectly through bulk collision sequences. In the case where the component of the transferred momentum normal to the surface is sufficiently large, the atom will be sputtered off the surface leaving a surface vacancy behind. Surface collision sequences propagating along close-packed directions in the surface shown in Figure 21 may be excited by momentum transfer to neighboring atoms—a process that is favored by the angular dependence of the Rutherford scattering cross-section. Under prolonged irradiation, the surface vacancies will move around by irradiation-induced diffusion and may agglomerate to form pits. Surface collision sequences ending at a descending surface step or at a hole or groove, on the other hand, may generate a surface adatom, leaving a surface vacancy at or near its point of departure. Adatoms created on the surfaces of grooves will in general reduce the groove surface area. Since the propagation of collision sequences is highly anisotropic, this may lead to a gradual alignment of the grooves and pits under prolonged irradiation. This process is similar to that of the formation of lattices of stacking-fault tetrahedra under high-dose electron irradiation [12,13]. Such a mechanism can work only if the mobility of the surface vacancies is not too large. This probably accounts for the fact that regular groove patterns have so far been observed for Au only after low-temperature irradiation but not under room-temperature irradiation conditions.

temperature irradiation but not under room-temperature irradiation conditions.

angular dependence of the Rutherford scattering cross-section. Under prolonged irradiation, the surface vacancies will move around by irradiation-induced diffusion and may agglomerate to form pits. Surface collision sequences ending at a descending surface step or at a hole or groove, on the other hand, may generate a surface adatom, leaving a surface vacancy at or near its point of departure. Adatoms created on the surfaces of grooves will in general reduce the groove surface area. Since the propagation of collision sequences is highly anisotropic, this may lead to a gradual alignment of the grooves and pits under prolonged irradiation. This process is similar to that of the formation of lattices of stacking-fault tetrahedra under high-dose electron irradiation [12,13]. Such a mechanism can work only if the mobility of the surface vacancies is not too large. This probably accounts for the fact that regular groove patterns have so far been observed for Au only after low-

**Figure 21.** Movement of vacancy due to momentum transfer along close-packed direction. White circle indicates surface vacancy. (**a**) Collision of electron, (**b**) momentum transfer along close packed direction given by the collision of electron, (**c**) movement of surface vacancy opposite to the direction of momentum transfer along close packed direction. **Figure 21.** Movement of vacancy due to momentum transfer along close-packed direction. White circle indicates surface vacancy. (**a**) Collision of electron, (**b**) momentum transfer along close packed direction given by the collision of electron, (**c**) movement of surface vacancy opposite to the direction of momentum transfer along close packed direction.

Additionally, one should note that the pattern of aligned nanogroove for the 400 keV electron irradiation for Au (Figure 2) is clearer than the one for the 800 keV electron irradiation (Figure 4). The origin of the less clear pattern in the latter case should be attributed to some additional effects such as a complicated sputtering process; that is, at energies <600 keV, surface atoms are sputtered by direct recoils only, whereas at energies >600 keV, up to about 10% of the total yield comprises surface atoms sputtered by sub-surface recoils [23] and the formation of Frenkel pairs, which can occur at higher irradiation energy of electrons [24]. Angular distributions of sputtered atoms as a function of electron energy [23] may affect the formation of adatoms and the pattern formation. Moreover, the formation of aligned nanogrooves and nanoholes are significantly affected by the irradiation temperature (Figures 9 and 10), probably reflecting the mobility of surface vacancy. Additionally, one should note that the pattern of aligned nanogroove for the 400 keV electron irradiation for Au (Figure 2) is clearer than the one for the 800 keV electron irradiation (Figure 4). The origin of the less clear pattern in the latter case should be attributed to some additional effects such as a complicated sputtering process; that is, at energies <600 keV, surface atoms are sputtered by direct recoils only, whereas at energies >600 keV, up to about 10% of the total yield comprises surface atoms sputtered by subsurface recoils [23] and the formation of Frenkel pairs, which can occur at higher irradiation energy of electrons [24]. Angular distributions of sputtered atoms as a function of electron energy [23] may affect the formation of adatoms and the pattern formation. Moreover, the formation of aligned nanogrooves and nanoholes are significantly affected by the irradiation temperature (Figures 9 and 10), probably reflecting the mobility of surface vacancy.

### **5. Conclusions**  We found a new type of self-organized nanostructure formation on the exit surface **5. Conclusions**

of thin gold foils irradiated with high doses of 360–1250 keV electrons at temperatures of about 100 K. The structure consists of aligned nanogrooves, which develop parallel to the surface, and nanoholes and hillocks, which grow parallel to the electron beam. The nanogrooves show strong irradiation-direction dependencies on their growth. They grow along [100] and [010] directions for [001] irradiation, along [100] for the [011] irradiation, whereas no clear grooves are formed for [111] irradiation. The widths of nanogrooves and holes are between about 1 and 2 nm, which are the smallest ones generated on metal surfaces so far. The final structures of the thin foils under electron irradiation are nanoparti-We found a new type of self-organized nanostructure formation on the exit surface of thin gold foils irradiated with high doses of 360–1250 keV electrons at temperatures of about 100 K. The structure consists of aligned nanogrooves, which develop parallel to the surface, and nanoholes and hillocks, which grow parallel to the electron beam. The nanogrooves show strong irradiation-direction dependencies on their growth. They grow along [100] and [010] directions for [001] irradiation, along [100] for the [011] irradiation, whereas no clear grooves are formed for [111] irradiation. The widths of nanogrooves and holes are between about 1 and 2 nm, which are the smallest ones generated on metal surfaces so far. The final structures of the thin foils under electron irradiation are nanoparticles or nanowires. This method has been utilized to produce long gold nanowires for investigations of the interesting physics such as the electron transport properties and the multi-shell structure. Temperature dependence of the nanostructure for gold indicates that the effect of surface diffusion becomes significant above 240 K.

Furthermore, the self-organized structures for silver, copper, nickel, and iron are investigated. The formation of nanoholes and nanogrooves basically originates in the sputtering at the electron exit surface. The difference in the anisotropic growth of the nanogrooves and nanoholes among the kinds of metals should be attributed to the irradiation-induced anisotropic flow of point defects and some related factors, which are attributed to the nature of metals. Thus, we can use the present investigation for the studies of irradiationinduced effects and the surface diffusion effect, of which knowledge should be useful for the synthesis of new nanomaterials.

**Funding:** This study was supported by fellowships from the Ministry of Education of Japan and Max-Planck-Institut.

**Acknowledgments:** I express my sincere thanks to Wilfried Sigle, Fritz Phillipp, the late Alfred Seeger, and Hiroaki Abe for their collaboration. Experimental works were mostly done in Max-Planck-Institut für Metallforschung and partly Japan Atomic Energy Research Institute-Takasaki.

**Conflicts of Interest:** The authors declare no conflict of interest.
