## 4 Discussion  
The as-built microstructure of the L-PBF Ti6 Al4V-ELI samples (Figure 4) is characterized by columnar \(\beta\)-grains that grow parallel to the \(z\)-axis, or perpendicular to the xy plane, following the heat fluxes developed during the L-PBF process [55; 56]. The \(\beta\)-grains nucleate from the build platform and grow across each of the deposited layers along the \(<\)100\(>\) as shown in Figure 4a [57]. As a matter of fact, the columns are arranged perpendicular to the molten pools. At the same time, they are contained within the laser scan tracks on the xy plane, as shown in Figure 4b. This configuration of the columnar \(\beta\)-grains characterized all samples regardless of the build orientations (Figures 4a and 5) [58]. The fully columnar structure is also confirmed by the relationships between the thermal gradient (G, (K/m)) and the solidification rate (R, (m/s)), which characterized the Ti6 Al4V alloy during the L-PBF process [12]. In addition, the complex thermal history and the high cooling rate that characterized the L-PBF process induced the formation of \(\alpha^{\prime}\)-martensite, arranged in a hierarchical structure wherein the major axis of the primary \(\alpha^{\prime}\) formed an angle of 45\({}^{\circ}\) with respect to the \(\beta\)-grain boundary [12; 59; 60; 61]. [PERSON] et al. [60] also affirmed that the \(\alpha^{\prime}\)-martensite forms an angle of 30 or 60\({}^{\circ}\) or 30 to 60\({}^{\circ}\) with respect to the build orientation. In the same context, [PERSON] et al. [32] showed angles of 30, 60 and 90\({}^{\circ}\) between different  
Figure 13: HV\({}_{0.1}\) indentations performed on different microstructures of the heat-treated 1050 \({}^{\circ}\)C/60\({}^{\prime}\): (**a–d**) 90\({}^{\circ}\)\({}_{x}\)-bar and (**e,f**) 90\({}^{\circ}\)\({}_{x}\)-tensile sample. \(\alpha^{\prime}\)-laths. This hierarchical structure of the \(\alpha^{\prime}\)-martensite remains in the \(\alpha\)-laths developed after the heat treatments at 704 and 740 \({}^{\circ}\)C. Likewise, the columnar shape of the prior \(\beta\)-grains is also retained after those heat treatments. In particular, the \(\alpha+\beta\) microstructure developed after the treatment below the \(\beta\)-transus presents primary, secondary and tertiary \(\alpha\)-phase arranged along the same orientations as the progenitor \(\alpha^{\prime}\)-martensite laths. [PERSON] et al. [29] confirmed the absence of quartic \(\alpha\)-laths due to the \(\alpha^{\prime}\)-martensite \(\rightarrow\beta\) decomposition. The XRD spectra, shown in Figure 8a, confirm a possible partial \(\alpha^{\prime}\rightarrow\alpha+\beta\) transformation due to the presence of peaks related to the \(\beta\) phase, which are absent on the as-built XRD spectra [12]. TEM analysis discussed by [PERSON] et al. [62], which was performed on the same heat-treated samples, confirmed the presence of \(\alpha^{\prime}\)martensite and, therefore, the incomplete \(\alpha^{\prime}\rightarrow\alpha+\beta\) transformation. Therefore, this validates the \(\alpha^{\prime}\)/\(\alpha\)-phase labels shown on the XRD patters related to the samples heat-treated at 704 \({}^{\circ}\)C/120\({}^{\prime}\) and at 740 \({}^{\circ}\)C/130\({}^{\prime}\), respectively. Because the \(\alpha+\beta\) microstructure retains much of the features of the pristine \(\alpha^{\prime}\)-martensite, the mechanical properties of both the heat-treated samples at 704 and 740 \({}^{\circ}\)C do not vary significantly (Figure 11 and Table 5). Therefore, the increase in the average thickness of the \(\alpha\)-laths from (540 \(\pm\) 60) to (700 \(\pm\) 10) nm, which can be caused by both the higher heat-treatment temperature and the first step of cooling up to 520 \({}^{\circ}\)C in 90\({}^{\prime}\), does not influence the mechanical performance.