## 2 Materials and Methods  
### Sample Preparation  
The samples were obtained from a cylindrical bar of Ti-6 Al-4V alloy with a predominantly \(\alpha+\beta\) microstructure. The alloy used in this study was Ti-6 Al-4V ELI (Extra Low Interstitial), a variant specifically developed for biomedical applications due to its reduced interstitial content and enhanced biocompatibility. This material complies with internationally recognized standards for surgical implants, such as ASTM F136 [51] and ISO 5832-3 [52], ensuring its suitability for use in load-bearing biomedical devices. In \(\alpha+\beta\) titanium alloys, the \(\alpha\) phase has a hexagonal close-packed (HCP) crystal structure and contributes to thermal stability, corrosion resistance, and high mechanical strength. The \(\beta\) phase, with a body-centered cubic (BCC) structure, enhances ductility, formability, and toughness. The relative volume fraction of these phases depends on the thermomechanical processing. In Ti-6 Al-4V ELI, which is widely applied in biomedical devices, the \(\beta\) phase typically ranges from 5% to 30% by volume, providing a favorable combination of fatigue resistance, strength, and biological compatibility [53]. The samples were fabricated in the desired dimensions using conventional machining by cutting and turning to serve as electrodes in the experiments. Facing and finishing operations were carried out on the frontal face of the electrode for the flattening operation. The dimensions of the workpiece electrode were 9.5 mm in diameter and 12.0 mm in height, and the diameter of the tool electrode was 15.0 mm with 95.0 mm in height. Two samples from each experimental condition were sectioned along their longitudinal axis, perpendicular to the face, and repositioned before being machined using electrical discharge machining (EDM), to analyze the modifications at the lateral section. The chemical composition of the material is presented in Table 1.  
Furthermore, a cylindrical graphite bar was used for the tool electrode, and two different dielectric fluid conditions were employed in the experiment. The first, termed DF1-F was an aqueous solution containing 0.10 M of hydrofluoric acid (HF) and 0.20 M of phosphoric acid (H\({}_{3}\)PO\({}_{4}\)), with a final pH of 1.5. The second termed as DF2-Ca was an aqueous solution containing 0.05 M of calcium dichloride dihydrate (CaCl\({}_{2}\).2H\({}_{2}\)O) and 0.03 M of sodium phosphate monobasic monohydrate (NaH\({}_{2}\)PO\({}_{4}\).H\({}_{2}\)O), acidified with 37% hydrochloric acid (HCl) to reach a final pH of approximately 3.5. Both solutions were prepared using reagent-grade chemicals and deionized (DI) water. These fluids were selected for their ability to enrich the surface with elements such as oxygen, phosphorus, and calcium, all of which are known to enhance osseointegration in biomedical applications [50; 54]. After EDM processing, they were completely eliminated from the samples through post-processing cleaning and sterilization procedures. Specifically, for the tests performed with DF1-F, which contains fluorine, a small dielectric reservoir was used to prevent corrosion in the main tank, similar to previous studies [49]. A die sinking type EDM machine (ELETROPLUS EDM-540, from SERVSPARK manufacturer) was used to carry out the experimentation. Experiments involved two different discharge polarities in separate experiments. One with negative polarity (i.e., the tool electrode (\(-\)) and work piece (\(+\))) and another with positive polarity (i.e., the tool electrode (\(+\)) and work piece (\(-\))). The use of both negative and positive polarities was based on the understanding that discharge polarity significantly affects the electrical discharge machining (EDM) process. Including both conditions may allow for the evaluation of how polarity influences not only surface morphology but also the incorporation of bioactive elements and biocompatibility [50].