3.1.4. Annealing of the Nanostructure at Room Temperature

Figure 8a,b, respectively, show an area of Au foil irradiated along [111] at 800 keV with a fluence of about 8 × 1026 electrons m−2 and annealed at room temperature. Both the photos were observed obliquely from [001] direction, by tilting the specimen from the irradiation direction. The projection of the electron-beam direction during irradiation is indicated by an arrow in Figure 8a, and nanoholes are observed with parallel dark lines. They appear to develop rather randomly under [011] irradiation but grow along the irradiation direction under [111] irradiation [18]. The dark features are hillocks developing

along the irradiation directions. On room-temperature annealing, the nanoholes become thermally unstable irrespective of the original irradiation direction. They transform to voids with large diameters, while the hillocks decrease in height, as seen in Figure 8b. diation direction under [111] irradiation [18]. The dark features are hillocks developing along the irradiation directions. On room-temperature annealing, the nanoholes become thermally unstable irrespective of the original irradiation direction. They transform to voids with large diameters, while the hillocks decrease in height, as seen in Figure 8b.

Figure 8a,b, respectively, show an area of Au foil irradiated along [111] at 800 keV with a fluence of about 8 × 1026 electrons m−2 and annealed at room temperature. Both the photos were observed obliquely from [001] direction, by tilting the specimen from the irradiation direction. The projection of the electron-beam direction during irradiation is indicated by an arrow in Figure 8a, and nanoholes are observed with parallel dark lines. They appear to develop rather randomly under [011] irradiation but grow along the irra-

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3.1.4. Annealing of the Nanostructure at Room Temperature

**Figure 8.** TEM micrographs of an area of Au foil (**a**) irradiated along [111] direction at 800 keV with a fluence of about 8 × 1026 electrons m−2 then (**b**) annealed at room temperature. Both the photos were taken along [001] direction. The projection of the electron-beam direction during irradiation is shown by a black arrow in photo (**a**). Voids transformed from nanoholes are indicated by arrows in photo (**b**). **Figure 8.** TEM micrographs of an area of Au foil (**a**) irradiated along [111] direction at 800 keV with a fluence of about 8 × 1026 electrons m−2 then (**b**) annealed at room temperature. Both the photos were taken along [001] direction. The projection of the electron-beam direction during irradiation is shown by a yellow arrow in photo (**a**). Voids transformed from nanoholes are indicated by arrows in photo (**b**).

#### 3.1.5. Irradiation Temperature Dependence on the Structure 3.1.5. Irradiation Temperature Dependence on the Structure

To know the irradiation temperature dependence on the formation of nanostructure, we investigated the structural change under electron irradiation at several different temperatures. Figure 9 shows bright-field images of Au(001) foils irradiated along [001] direction at four different temperatures. The electron irradiations were done with a beam of several hundred nm in diameter, and observation were done in areas where the structure looks homogeneous. The flux density is about 2 × 1024 electrons m−2 s−1. To know the irradiation temperature dependence on the formation of nanostructure, we investigated the structural change under electron irradiation at several different temperatures. Figure 9 shows bright-field images of Au(001) foils irradiated along [001] direction at four different temperatures. The electron irradiations were done with a beam of several hundred nm in diameter, and observation were done in areas where the structure looks homogeneous. The flux density is about 2 × 1024 electrons m−2 s −1 .

 One should note that the density of nanohole is almost constant over the irradiated dose range at each irradiation temperature [11]. Then, the difference in the time indicated in Figure 9 does not significantly affect the investigation on the temperature dependence of the density of nanoholes.  One should note that the density of nanohole is almost constant over the irradiated dose range at each irradiation temperature [11]. Then, the difference in the time indicated in Figure 9 does not significantly affect the investigation on the temperature dependence of the density of nanoholes.

Figure 10 shows the Arrhenius plot of the density of nanoholes. We can find two lines with apparent activation energy of 0.0046 eV below 240 K and 0.088 eV above 240 K. Similar studies were done several decades ago by Cherns [11]. He gave in situ observation of sputtering at 1.0 MeV with thin (111) gold films by using the Harwell EM7 high-voltage electron microscope. He measured the pit density, which corresponds to the nanohole density in the present study, against the irradiation temperature and found a temperature dependence on the pit density. However, he could not measure the pit densities greater than about 1–2 ×1016 m−2 , owing to a limit in the image resolution between adjacent pits. In the present study, we used JEOL-1250 transmission electron microscope, and the resolution is enough high to determine the density below 273 K, as seen in Figure 10.

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**Figure 9.** Au(001) foils irradiated along the [001] direction with 1250 keV electrons. (**a**) 110 K, 1070 s; (**b**) 240 K, 2130 s; (**c**) 270 K, 1180 s; (**d**) 300 K, 2680 s. **Figure 9.** Au(001) foils irradiated along the [001] direction with 1250 keV electrons. (**a**) 110 K, 1070 s; (**b**) 240 K, 2130 s; (**c**) 270 K, 1180 s; (**d**) 300 K, 2680 s. In the present study, we used JEOL-1250 transmission electron microscope, and the resolution is enough high to determine the density below 273 K, as seen in Figure 10.

**Figure 10.** Arrhenius plot of the density of nanoholes. Two linear relations are seen, giving appar-**Figure 10.** Arrhenius plot of the density of nanoholes. Two linear relations are seen, giving apparent activation energies of 0.0046 eV below 240 K and 0.088 eV above 240 K.

**Figure 10.** Arrhenius plot of the density of nanoholes. Two linear relations are seen, giving apparent activation energies of 0.0046 eV below 240 K and 0.088 eV above 240 K. Cherns proposed a theoretical model in which pits form by the diffusion and agglomeration of surface vacancies produced by sputtering. The model explains the experimental results in some detail, and the apparent activation energy of pit density against 1/T is suggested to take a value of Em/3, where Em is the migration energy of surface vacancy. Utilizing Cherns' model in the present result on the density of pits on Au(001), the migration energy of a surface vacancy on Au(001) is derived to be 0.26 eV with the apparent activation energy of 0.088 eV shown in Figure 10. The value is lower than Em = 0.45 eV given by Cherns, but almost in the range of error bar. If the apparent activation energy of 0.088 eV above 240 K were to relate to the migration of vacancy, a following question remains; "what is the activation process for the lower value of 0.0046 eV below 240 K?", which has not been found by Cherns. We can guess that the activation energy below 240 K may relate to the migration of adatom, etc., but further experimental and theoretical studies are awaited.

ent activation energies of 0.0046 eV below 240 K and 0.088 eV above 240 K.

### *3.2. Comparison among Gold, Silver, and Copper 3.2. Comparison Among Gold, Silver, and Copper*

awaited.

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Figure 11 compares nanostructure, which appeared for Au(001), Ag(001), and Cu(001) foils irradiated with 400 keV electrons along [001] at 95 K [21]. Elongated bright images correspond to grooves formed on the electron exit surface of the foils. One can see that the patterns of grooves for both Ag and Cu are not as clear as the one for Au and extend weakly along [110] and [110] directions. The width of grooves for Cu is about 2–4 nm, significantly larger than those for Au and Ag, which are about 1–2 nm. Figure 11 compares nanostructure, which appeared for Au(001), Ag(001), and Cu(001) foils irradiated with 400 keV electrons along [001] at 95 K [21]. Elongated bright images correspond to grooves formed on the electron exit surface of the foils. One can see that the patterns of grooves for both Ag and Cu are not as clear as the one for Au and extend weakly along [110] and [11 0] directions. The width of grooves for Cu is about 2– 4 nm, significantly larger than those for Au and Ag, which are about 1–2 nm.

Cherns proposed a theoretical model in which pits form by the diffusion and agglomeration of surface vacancies produced by sputtering. The model explains the experimental results in some detail, and the apparent activation energy of pit density against 1/T is suggested to take a value of Em/3, where Em is the migration energy of surface vacancy. Utilizing Cherns' model in the present result on the density of pits on Au(001), the migration energy of a surface vacancy on Au(001) is derived to be 0.26 eV with the apparent activation energy of 0.088 eV shown in Figure 10. The value is lower than Em = 0.45 eV given by Cherns, but almost in the range of error bar. If the apparent activation energy of 0.088 eV above 240 K were to relate to the migration of vacancy, a following question remains; "what is the activation process for the lower value of 0.0046 eV below 240 K?", which has not been found by Cherns. We can guess that the activation energy below 240 K may relate to the migration of adatom, etc., but further experimental and theoretical studies are

**Figure 11.** Nanostructures generated on (**a**) Au(001), (**b**) Ag(001), and (**c**) Cu(001) foils under 400 keV electron irradiation along [001] direction at 95 K. The patterns of grooves for both Ag and Cu are not as clear as the one for Au. The width of grooves for Cu is about 2–4 nm, significantly larger than those for Au and Ag, which are about 1–2 nm. **Figure 11.** Nanostructures generated on (**a**) Au(001), (**b**) Ag(001), and (**c**) Cu(001) foils under 400 keV electron irradiation along [001] direction at 95 K. The patterns of grooves for both Ag and Cu are not as clear as the one for Au. The width of grooves for Cu is about 2–4 nm, significantly larger than those for Au and Ag, which are about 1–2 nm.

Contrary to the differences in the patterns for [001] irradiation, the groove formed by the oblique irradiations along [011] direction for Au, Ag, and Cu show a preferential elongation along [100], as denoted by arrows in Figure 12a–c. Note that the Ag specimen has a wavy surface. Then, the grooves formed on the surface are uneven and denuded in some areas, similar to the case of an Au foil with grain boundaries [11] but tend to grow along [100] in spite of the wavy surface. In addition to nanogrooves developed parallel to the exit surface of foils, nanoholes and hillocks are formed, as seen for Au, Ag, and Cu foils in Figure 13a–c, respectively [21]. The irradiations were done with 400 keV electrons at 95 K, and the photos were taken obliquely against the beam direction. Elongated images de-Contrary to the differences in the patterns for [001] irradiation, the groove formed by the oblique irradiations along [011] direction for Au, Ag, and Cu show a preferential elongation along [100], as denoted by arrows in Figure 12a–c. Note that the Ag specimen has a wavy surface. Then, the grooves formed on the surface are uneven and denuded in some areas, similar to the case of an Au foil with grain boundaries [11] but tend to grow along [100] in spite of the wavy surface. In addition to nanogrooves developed parallel to the exit surface of foils, nanoholes and hillocks are formed, as seen for Au, Ag, and Cu foils in Figure 13a–c, respectively [21]. The irradiations were done with 400 keV electrons at 95 K, and the photos were taken obliquely against the beam direction. Elongated images denoted by arrows correspond to nanoholes growing from the exit surface and dark contrasts denoted by **h** are hillocks. The directions of the growth of nanoholes and hillocks are along and opposite to the irradiation direction, respectively. One should note that the nanoholes grow deeper than 10 nm with an almost constant diameter of about 1–2 nm for Au and Ag and about 2–4 nm for Cu. Most of the nanoholes are formed in the areas of nanogrooves. The images of nanoholes observed along the irradiation direction can be found as extremely bright spots in Figure 12.

found as extremely bright spots in Figure 12.

found as extremely bright spots in Figure 12.

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**Figure 12.** TEM images of nanostructure generated on the exit surface of Au, Ag, and Cu foils irradiated with 400 keV electrons along [011] direction at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001), 510 s; (**c**) Cu(001), 2160 s. Nanogrooves with bright contrast are seen to elongate along [100] direction for all the cases. **Figure 12.** TEM images of nanostructure generated on the exit surface of Au, Ag, and Cu foils irradiated with 400 keV electrons along [011] direction at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001), 510 s; (**c**) Cu(001), 2160 s. Nanogrooves with bright contrast are seen to elongate along [100] direction for all the cases. **Figure 12.** TEM images of nanostructure generated on the exit surface of Au, Ag, and Cu foils irradiated with 400 keV electrons along [011] direction at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001), 510 s; (**c**) Cu(001), 2160 s. Nanogrooves with bright contrast are seen to elongate along [100] direction for all the cases.

noted by arrows correspond to nanoholes growing from the exit surface and dark contrasts denoted by **h** are hillocks. The directions of the growth of nanoholes and hillocks are along and opposite to the irradiation direction, respectively. One should note that the nanoholes grow deeper than 10 nm with an almost constant diameter of about 1–2 nm for Au and Ag and about 2–4 nm for Cu. Most of the nanoholes are formed in the areas of nanogrooves. The images of nanoholes observed along the irradiation direction can be

noted by arrows correspond to nanoholes growing from the exit surface and dark contrasts denoted by **h** are hillocks. The directions of the growth of nanoholes and hillocks are along and opposite to the irradiation direction, respectively. One should note that the nanoholes grow deeper than 10 nm with an almost constant diameter of about 1–2 nm for Au and Ag and about 2–4 nm for Cu. Most of the nanoholes are formed in the areas of nanogrooves. The images of nanoholes observed along the irradiation direction can be

and Cu foils irradiated with 400 keV electrons at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001) 600 s; (**c**) Cu(001), 3180 s. All images were taken oblique to the irradiation directions. Nanoholes and hillocks denoted by arrows and by **h** are seen to elongate opposite to and along the beam direction, respectively. **Figure 13.** TEM images of deep nanoholes and hillocks generated on the exit surface of Au, Ag, and Cu foils irradiated with 400 keV electrons at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001) 600 s; (**c**) Cu(001), 3180 s. All images were taken oblique to the irradiation directions. Nanoholes and hillocks denoted by arrows and by **h** are seen to elongate opposite to and along the beam direction, respectively. **Figure 13.** TEM images of deep nanoholes and hillocks generated on the exit surface of Au, Ag, and Cu foils irradiated with 400 keV electrons at 95 K: (**a**) Au(001), 600 s; (**b**) Ag(001) 600 s; (**c**) Cu(001), 3180 s. All images were taken oblique to the irradiation directions. Nanoholes and hillocks denoted by arrows and by **h** are seen to elongate opposite to and along the beam direction, respectively.


*4.3. Strengths and Limitations*

A major strength of our study is that physical fitness, body height, weight, and fat percentage were objectively measured by trained staff according to standardized methods. In addition to the large sample and the number of determinants analyzed, further strength is the utilization of a weight-specific HRQOL-measurement tool that has been shown to have good psychometric properties.

The primary limitation of our study is the cross-sectional design, which does not allow any conclusions to be drawn regarding the causal direction of the relationship between the observed variables. Furthermore, several obesity-relevant factors were not included due to incomplete data such as dietary habits, type of school, single parenting, and parents' BMI. The inclusion of these limited data would have resulted in too great a sample size restriction. As such, there may be additional factors that could confound the association between the independent variables. Selection bias, information bias, and social desirability bias, that is, in self-reports on physical activity and media consumption, are further limitations. As a treatment-seeking population, the participants potentially shared characteristics, such as motivation, that distinguished them from other groups. Besides this, as some data were self-reported, the study is not free from information bias.