Projection of phase diagram. 44 Four states of matter are shown: solid, liquid, gas and plasma, as well as the metastable liquid phase and the two phase region. The normal melting temperature ( ), the critical temperature ( ), and the critical point (CP) are indicated. The phase boundaries are represented by the melting and sublimation curves, binodal (thick line), and spinodal (thin line) and the two dashed lines at and , respectively. The liquid parts of the binodal (diamonds) and the spinodal (circles) are depicted.
Schematic representation of Knudsen layer. The Knudsen layer (solid line) connects the target (dashed) and the ambient environment (dashed-dotted); here, the expanding copper plume. Properties at the surface (S) and at the end of the Knudsen layer (K) are indicated. The mass density, temperature, pressure, and velocity are denoted by ρ, T, P, and u, respectively. The properties at the surface are taken at the liquid part of the binodal (bn) (see also Fig. 1 ).
Schematic representation of bubble formation in the subcritical state. Spherical nuclei with a critical radius are indicated. At any time, the liquid pressure will tend to adjust itself to the ambient pressure . Bubble growth is now controlled by the ratio of the pressures outside the bubble (liquid pressure ) and inside the bubble (bubble pressure ). Since a hydrocode calculates physical properties that are spatially averaged over each computational cell, the model will provide average bubble sizes (dashed).
Projection of phase diagram for temperatures between and . The path of a surface cell is shown for 7.8–9.6 ns for the given conditions (box). Material heating (red squares) as well cooling (blue triangles) is observed. The two isobars (dashed) at 0 and 2 GPa, respectively, define the region of material evolution.
(a) Temporal profile of original ( ) and actual ( ) laser intensities arriving at the target surface as well as the surface temperature . (b) Temporal profile of the pressure ratio across the bubble and the ambient pressure.
(a) Temporal evolution of the reflectivity R (solid line) and the surface temperature (dashed). Note that both profile shapes can be mirrored due to the fact that the reflectivity decreases with increasing temperature. (b) Spatial profile of the temperature (black, thick line), mass density ρ (black, thin line), and the thermal conductivity κ (red dashed) at instant 11 ns. Note that the surface temperature acquires its maximum value in the second peak of the bimodal pattern at that instant (see (a)). The discontinuity in the thermal conductivity and mass density can be attributed to the phase change at the melting point .
Temporal profiles of original ( ) (black, thick solid line) and actual ( ) (black, thin solid line) measured laser intensities at the copper surface are compared with the corresponding calculated laser intensities (red, dashed-dotted and red, dashed, respectively). The arrows indicate the onset time of laser induced breakdown. Two situations are depicted: (a) and (b) ). The respective calculated onset times of laser induced breakdown are indicated.
(a) Comparison of calculated and experimental transmissivities vs fluence. (b) Comparison of calculated and experimentally ablated depths vs fluence. The results of two model settings are shown: considering only surface mechanisms (diamonds), and accounting for both surface and volumetric mass removal (crosses).
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