**4.2 Boundary and initial conditions**

The contours of the wall are calculated by the following equation:

$$\sqrt{\frac{\chi^2}{a^2} + \frac{y^2}{b^2}} = 1\tag{16}$$

where, *a* and *b* are constants with a relation of *a b* 1 52 .

For the boundary conditions, non-slip conditions are applied to the cell wall, except for the position of the plume ejection. Outgoing flow conditions are applied to the boundaries outside the cell. The position of the plume ejection is set at one of the focal points of the ellipsoidal cell. The sudden ejection generates a traveling shock wave which is converges at the other focal point. The cell exit, through which the flow passes during the propagations of the shock and pressure waves, connects the inside and outside of the cell. During the focusing process of the propagating shock wave, the interaction between the converging shock wave and plume plays an important role in the growing nanoparticle size. An ejected jet of gas is shut off after a certain period so that the calculation can be used for a basic reference for PLA techniques. Then, the ejected gas is considered to be a plume traveling toward the exit of the cell on the right side wall. It is clear that many parameters are involved in this process. We have chosen the three main parameters to be the Mach number, jet duration, and diameter of the exit hole, because, in related experiments, the controllable

Thermodynamics of Nanoparticle Formation in Laser Ablation 137

converged at the focal point, it began to spread out again. Most of the spreading shock wave, except for the left traveling shock wave, impinged on the wall again (Figure 7(d)). The shock wave around the exit hole causes weak compression waves to be transmitted into the cell through the hole. After the spreading shock wave was reflected from the wall again (Figure 7(e)), it started to converge at the focal point, where the plume is already present. Then, the shock wave, having been through two reflections, is strong enough to deform the plume and flatten the vortices. The deformed plume front still has enough momentum to transmit through the exit hole (Figure 7(f)). However, part of the plume is left in the cell due to the small diameter of the exit hole. Figure 7(f) suggests that the exit diameter is an important factor in evaluating how much of the plume can get through the exit hole. By choosing the suitable size of exit hole, we can efficiently extract the plume, which once converged at the focal point of the ellipsoidal cell. If these suitable conditions are applied to the actual laser ablation process in the ellipsoidal cell, the laser ablated plume can be confined by a converging shock wave followed by a generation of monodispersed

The main part of the experimental setup, shown in Figure 8, is composed of the generation and deposition chamber. The laser beam is introduced into the generation chamber. The laser plume is confined by the ellipsoidal cell and uniform-sized nanoparticles are generated. An ambient gas is supplied into the ellipsoidal cell and the cell is filled with the gas. The deposition chamber is connected to the generation chamber through a skimmer, where the nanoparticles are extracted by the ambient gas flow. A substrate is placed in a

Fig. 8. Schematic diagram of the apparatus for the nanoparticle formation using Pulsed

When the high-power pulsed laser is directed onto a solid sample in the ellipsoidal cell filled with the ambient gas, the plume is ejected perpendicular to the sample surface. At that time, a shock wave is also generated, driven by the plume expansion, and then propagates in the ambient gas. By placing the sample surface on the focal point of the ellipsoidal cell, the shock wave is reflected on the inner wall of the cell and focused onto the other focal point.

nanoparticles.

Laser Ablation

**5. Experimental results 5.1 Experimental equipment** 

vertical position for the deposition of the nanoparticles.

parameters are the laser power, duration of the laser pulse, and diameter of the cell exit hole. We therefore assume that the experimental parameters related to the laser power and pulse correspond to the jet Mach number and jet duration, respectively. Hence, we have selected the above three parameters to be tested, fixing all the other parameters. The states of the gas inside and outside of the cell are initially at rest, that is, the ambient properties such as the pressure, density, temperature are uniform over the whole calculation region.

Fig. 7. Time variations of density contours in the ellipsoidal cell.
