## 3 Results and Discussions
### X-Ray Diffraction Analysis  
Figure 9 presents the results of the XRD phase analysis of the AZ63 magnesium alloy and of the PEO coatings obtained in 10 g/L NaAlO\({}_{2}\) for a process duration of 5 min (AZ63_5m), 10 min (AZ63_10m) and 20 min (AZ63_20m). At the bottom of Figure 9, one can see a typical XRD pattern of an AZ63 magnesium alloy, with results consistent with other reports [19; 25]. It shows high-intensity lines related to the Mg \(\alpha\)-matrix (DB card 04-006-2605) and some Mg\({}_{17}\)Al\({}_{12}\)\(\beta\)-phase (DB card 04-010-7477) less-intense XRD lines. XRD data show that all the PEO treated samples are composed mainly of MgAl\({}_{2}\)O\({}_{4}\) (DB card 04-007-4175), with a minor contribution from the MgO (DB card 01-076-2583) crystalline phase. Due to the porosity and limited thickness of the coatings, line profiles associated with the substrate are also present in the diffraction patterns of the coated samples. The magnesium alloy diffraction lines' intensity decreases with processing time, suggesting the formation of thicker coatings. No Zn specific crystalline phase was detected. The formation of MgAl\({}_{2}\)O\({}_{4}\) as a majority coating constituent is promoted by substrate [26] and electrolyte composition [39]. XRD patterns of the coatings detached from the magnesium alloy according to the procedure described in Section 2.2, are shown in Figure 10. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Coating Thickness (\(\upmu\)m)** & **Barrier Layer Thickness (\(\upmu\)m)** \\ \hline AZ63\_5m & 15.14 \(\pm\) 4.21 & 0.36 \(\pm\) 0.06 \\ AZ63\_10m & 23.78 \(\pm\) 11.64 & 0.66 \(\pm\) 0.08 \\ AZ63\_20m & 36.60 \(\pm\) 9.22 & 0.67 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Coating and barrier layer mean thickness. Figure 9: XRD patterns of AZ63 magnesium alloy and coated samples. Better XRD resolution and the powder state of the coatings allowed the identification, aside from the spinel and the oxide crystalline phases, of another possible constituent crystalline phase--\(\gamma\)-Al\({}_{0.667}\)O (a non-stoichiometric \(\gamma\)-Al\({}_{2}\)O\({}_{3}\) phase, DB card number 04-016-1445). The position of the diffraction peaks from PDF cards used for qualitative phase analysis are presented in Appendix A (Figures A1-A7). Assuming the correct identification of the alumina crystalline phase, the quantitative phase analyses and microstructural parameters refined by the Rietveld method are presented in Table 6.  
The Rietveld analysis results indicate an increase in MgAl\({}_{2}\)O\({}_{4}\) coating content with processing time. [PERSON] et al. [40] showed that an increased concentration of sodium aluminate in the electrolyte can also lead to the formation of a larger amount of magnesium spinel by PEO processing of the AM50 alloy. Since the hardness of MgAl\({}_{2}\)O\({}_{4}\) is higher than the hardness of the periclase crystalline phase, an increased percent of magnesium spinel at the expense of MgO in the PEO coatings is of interest for applications that require hard coatings [41,42]. There is no correlation between processing time and the mean crystallite size, all the PEO coatings being nanostructured. Table 6 does not include microstructural parameters