# Femtosecond Laser Textured Surfaces for Radiative Cooling: Black Metals
## 3 Results and Discussion
### Ablation with High-Intensity fs-Laser Pulses  
Ablation experiments for W, Al, and Cu metals with the electron work functions: \(w_{e}=4.55\) eV (polycrystalline W), 4.06-4.2 eV (Al), 4.48-5.1 eV (different planes of Cu) were performed at the fundamental laser radiation wavelength of 1030 nm with a beam diameter on the surface of \(2r=60\)\(\upmu\)m. Hatching between adjacent lines was fixed at \(\Delta y=50\)\(\upmu\)m, which is slightly smaller than the focal diameter. For the tungsten sample (Figure 1a), the linear beam travel speed was set as \(v_{sc}=1000-25\) mm/s along the \(x\)-direction at a repetition rate of 100 kHz, producing pulse-to-pulse spacing of 10-0.2 \(\upmu\)m. The fluence per pulse was fixed at \(F_{p}=24.76\) J/cm\({}^{2}\) corresponding to the pulse energy of \(E_{p}=0.7\) mJ and the pulse duration of \(t_{p}=200\) fs; the average intensity per pulse is \(I_{p}=F_{p}/t_{p}=123.8\) TW/cm\({}^{2}\). A combination of the different pulse spacings with a single pass or five passes was performed. For aluminum and copper (Figure 1b,c), a total of 16 ablation areas were fabricated on each metal coupon's surface, defining the ablation matrix of the various pulse spacings  
Figure 2: **(a)** Reflectance of Al after ablation by 1030 nm/200 fs/0.1 MHz irradiation at different scanning speeds corresponding to different in-line separation between pulses \(\Delta x\) = (7–42) \(\upmu\)m (1-to-5) and different pulse energies \(E_{p}=0.8\) mJ (1) to 0.16 mJ (5). The focal spot size is \(\sim 60\)\(\upmu\)m; the inset photo shows a test matrix of 1 \(\times\) 1 mm\({}^{2}\) test fields. Polarisation on the sample is close to circular. The high emissivity \(E\geq 0.94\) of black body spray-coated samples with \(\sim\)0.2 mm thickness using Tasko TA410 KS dye was used for the reference. **(b)** SEM image of black-Al with typical surface of low-\(R\) in the IR spectral window; the fabrication condition: pulse spacing 14 \(\upmu\)m, fluence per pulse 28.3 J/cm\({}^{2}\). 42-7 \(\upmu\)m with different fluence per pulse 28.3-5.7 J/cm\({}^{2}\). Each ablated area, created under specific ablation conditions, was labeled with numbers (W: 1-6, Al: 1-16, Cu: 1-16) to align with the subsequent characterization results (Figure 1). The tested metals are very different in their physico-chemical properties. The molar enthalpy of vaporization (atomization) of Cu is 300 kJ/mol (338 kJ/mol), for Al 293 kJ/mol (326 kJ/mol), and for W 807 kJ/mol (849 kJ/mol), the highest among chemical elements). The enthalpy of vaporization recalculated per atom is 3.11 eV/atom (Cu), 3.04 eV/atom (Al), and 8.36 eV/atom (W). Solid densities for Cu of \(\rho_{Cu}=8920\) kg\(\cdot\)m\({}^{-3}\) (molar volume \(V_{m}^{(Cu)}=7.11\) cm\({}^{3}\) and molar mass \(M_{Cu}=63.546\) g/mol), Al of \(\rho_{Al}=2700\) kg\(\cdot\)m\({}^{-3}\) (\(V_{m}^{(Al)}=\frac{M_{Al}}{\rho_{Al}}=10\) cm\({}^{3}\) where molar mass \(M_{Al}=26.98154\) g/mol), and W of \(\rho_{W}=19280\) kg\(\cdot\)m\({}^{-3}\) (\(V_{m}^{(W)}=9.54\) cm\({}^{3}\) and molar mass \(M_{W}=183.84\) g/mol) were found. The ablation threshold for metals can be estimated by [PERSON]'s model for the pulse fluence [37]. According to it, the ablation is initiated by depositing energy to electrons equal to the material's binding energy and the electron work function [37]:  
\[F_{th}^{(m)}=\frac{3}{8}(\epsilon_{b}+w_{e})\frac{\lambda n_{e}}{2\pi}, \tag{1}\]  
where \(\epsilon_{b}\) is the binding energy or enthalpy of vaporization, \(w_{e}\) is the electron work function (escape energy from a metal), \(l_{s}=c/(\omega\kappa)\equiv\lambda/(2\pi\kappa)\) is the absorption depth (the skin depth) in the plasma with electron density \(n_{e}\) and refractive index \(n^{*}=n+i\kappa\) with \(c\) and \(\omega\) being the speed and cyclic frequency of light, respectively, and \(A\) is the absorption coefficient (for good metals \(A\approx\frac{2\omega l_{s}}{c}\)). To estimate the ablation thresholds, the smallest of the listed \(w_{e}\) [eV] and binding energy per atom \(\epsilon_{b}\) [eV] values were used.