Assessment of the boundary conditions for a thermal model of pulsed laser ablation

Abstract

An assessment of the boundary conditions for pulsed laser ablation is presented in the case where a thermal sputtering mechanism is relevant at the surface of the molten pool formed by the effect of irradiation. This paper deals with, in particular, the evaporation and boiling mechanisms when superheating effects are allowed to occur. The non-equilibrium character of the process at fluences enabling superheating plays a critical role in the rise of a large temperature gradient and subsurface temperature maximum even in the presence of surface boiling by vapour bubble nucleation.

A thermodynamic model of plasma generation by pulsed laser irradiation in vacuum

“…However, increasing further I beyond I ev considerably changes the physics of process, also as concerns the properties of the vapour phase. It has been already remarked in this respect [15] the importance of the surface gradient, respectively, ∇ 1 T | z=0 ≈ 0 or ∇ 1 T | z=0 = 0 depending on either equilibrium or nonequilibrium situation. Once again a simple order of magnitude estimate shows that these preliminary considerations compel to modify also the way to regard the onset of the ionization process of the ablation plume and the formation of plasma.…”

“…Let T s be the surface temperature of the molten pool, being in general T s T b because of the possible overheating. The discussion of the thermal field within λ and in the solid phase has been already carried out in [15]; for these reasons any reference to the boiling mechanism is limited in the following sections only to the surface aspects necessary to describe the formation and properties of the vapour plume. The model aims to simplify as much as possible the mathematical formalism thus focusing the most relevant physical aspects of the thermal sputtering process.…”

“…One infers therefore from equation (3.4) that ε b is initially negligible with respect to ρCvT b at I ≈ I ev , whereas increasing formation of bubbles is to be expected at I > I ev . Also, a more efficient energy dissipation mechanism is now allowed to occur within λ: in fact the convection rate v necessarily increases because a stronger inward liquid stream velocity is required to balance the outward flow of matter in the form of vapour bubbles; in other words v can increase just because it is now controlled also by the boiling driven mass conservation [15]. In conclusion, at near-threshold fluences the surface evaporation and boiling processes are still consistent with the condition ∇ 1 T | z=0 ≈ 0 and appear as equilibrium limit cases in correspondence to which the surface and vapour temperatures are reasonably expected both equal to T b .…”

“…The thermal mechanisms are described by modelling the temperature field induced by the laser irradiation, in particular as concerns some interesting non-equilibrium phenomena like the possible overheating of the molten phase. A paper recently published [15] has introduced a model to describe the thermal ablation process of a molten layer formed by pulsed laser irradiation. The main purpose of the model was to describe the surface evaporation and boiling in presence of overheating and to correlate the time and space profile of the laser pulse with the surface recession rate.…”

Thermodynamic modeling of pulsed-laser-induced ablation

“…Moreover the problem rises about how to describe with the Clausius-Clapeyron equation not only the surface evaporation mechanism, which is operating at all the fluences, but also its possible change to a volume mechanism like boiling, which requires fluences considerably higher than the so called "ablation threshold" . The energy and momentum conservation laws help to handle the mathematical aspects of the problem as already discussed in [1], where also the energy of formation of the vapour bubbles is taken into account. Here some semi-quantitative considerations show that the same conclusions can be also obtained in a merely intuitive way, thus concerning only the most relevant physical aspects of the problem.…”