*6.1. Temperature Rise in Al Nanoparticle Manipulation*

In Section 3.2, various types of manipulation of Al nanoparticles on the TEM specimen stage were explained. These were migration, bonding, rotation, revolution, and embedding of the nanoparticles, and the driving forces were explained as tangential and centripetal forces, as shown in Figure 4. Another possibility of manipulation is the temperature rise caused by electron irradiation to induce their movement. Xu and Tanaka [10] estimated the temperature rise at the stage as 10◦ C at most, based on Equation (1) using Fisher's theory [21]:

$$\text{Tm} - \text{Tg} = \text{r}^2 \text{I}\_0 \Delta \text{E} \{ \text{a}\_0 + \ln(\text{R}/\text{r})^2 \} / 4 \text{kz}, \tag{1}$$

where Tm is the maximum temperature of the carbon film, Tg is the temperature of the Cu support grid, namely Tm − Tg is the temperature rise by electron beam irradiation, r is the radius of the irradiation beam, I<sup>0</sup> is the intensity of the irradiation beam (10<sup>20</sup> e/cm<sup>2</sup> s), ∆E is the energy loss of the incident electron in the carbon film, when it is <1000 nm thick, a<sup>0</sup> is Euler's constant (0.5772), R is the distance between the irradiation beam centre and the Cu grid bar, k is the thermal conductivity of carbon, and z is the thickness of the carbon film (20 nm).

The heating effect in the localised area under the irradiation condition of 10<sup>20</sup> e/cm<sup>2</sup> s can be a minor effect, and the Lorenz force or the momentum transfer from electrons and ionised atoms is the major effect of the manipulation. This effect is clearly supported by the counterclockwise revolution caused by the magnetic field change, as shown in Figure 8 [8].
