## 2 Materials and Methods  
### Sample Preparation  
The experimental work was performed on samples fabricated using Inconel 939 powder, with its chemical composition detailed in Table 1. This nickel-chromium-based alloy offers a well-balanced combination of resistance to high temperatures, oxidation, and corrosion. However, its high content of alloying elements makes it particularly challenging to machine. Table 2 presents the mechanical properties of the alloy following production via the LPBF technique and subsequent heat treatment (HT), which vary depending on the chosen printing strategy. Small, paddle-like samples featuring symmetrical ends and a thickness of 1.2 mm were fabricated using the LPBF technique, as illustrated in Figure 1. The manufacturing process was carried out with the use of an EOS M 100 system (EOS GmbH, Krailling, Germany). The printing employed metal powder with particle sizes ranging from 15 to 40 \(\upmu\)m. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Element** & **Cr** & **Co** & **Ti** & **Al** & **C** & **Nb** & **Ta** & **W** & **Ni** \\ \hline Chemical composition [\%] & 22 & 19 & 4 & 2 & 0.2 & 1 & 1.4 & 1.9 & Balance \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of Inconel 939 [19]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Heat-Treated Condition** & \multicolumn{3}{c}{**As-Manufactured**} \\ \hline  & **Vertical** & **Horizontal** & **Vertical** & **Horizontal** \\ \hline Yield strength R\({}_{\text{p}0.2}\) [MPa] & 1100 & 1130 & 740 & 880 \\ Ultimate tensile strength R\({}_{\text{m}}\) [MPa] & 1500 & 1520 & 1090 & 1160 \\ Elongation & 13 & 11 & 28 & 24 \\ Hardness at room temperature ISO 6508 [21] & 48 & & 33 \\ Average density [g/cm\({}^{3}\)] & & 8.15 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of Inconel 939 printed by the LPBF method (ASTM E8/E8M [20]) [19]. The printer settings included  
* a rotation between layers of 67\({}^{\circ}\);
* a layer thickness of 20 \(\upmu\)m;
* a hatch distance of 50 \(\upmu\)m;
* a 5 mm width for scanning stripes with a 0.1 mm overlap;
* a build direction that is along the height of the sample (a laser exposure strategy developed by EOS to improve the quality of the material) [22]. Several laser power configurations were evaluated, resulting in volumetric energy density (E) values between 58 J/mm\({}^{3}\) and 91 J/mm\({}^{3}\). The sample shown in Figure 2, produced with E = 75J/mm\({}^{3}\)--selected as the optimal parameter for this study--demonstrated superior characteristics in terms of both density and hardness (ASTM E18 [20]). The heat treatment applied to the printed samples followed the procedure outlined by the manufacturer (BIBUS HOLDING AG, Fehraltorf, Switzerland) [22]. This process was executed in three steps: solution annealing at 1374 K for 4 h, followed by rapid air cooling, secondary annealing at 1000 \({}^{\circ}\)C for 6 h, and a final annealing phase at 800 \({}^{\circ}\)C for 4 h in a stirred argon atmosphere. During printing, the samples (Figure 1) were oriented vertically, aligned with the build direction. They were positioned in rows, maintaining an approximate gap of 1 mm between adjacent samples. The sample preparation process also included its smoothing through preliminary vibratory finishing. This stage followed LPBF printing and HT and was performed using a custom-designed station for processing small-sized components. Initial trials indicated that the most rapid material removal occurred under vibratory conditions with an amplitude of 1.4 mm and a frequency of 30 Hz. The samples were paired with stainless steel balls measuring 6 mm in diameter and subjected to a 4 h processing cycle without any fluid. The treatment duration was selected based on prior experimental studies [23]. After each hour of processing, the samples underwent a 10 min cleaning cycle in an ultrasonic bath.