## 2 Results and Discussion
the scattering of the resonant atoms (that is Au atoms, Figure 2 panels a and c; Pd atoms, panels b and d), the broad halo, which is particularly evident for measurements at the Pd K edge, should arise from the scattering of a palladium-rich phase formed by very small (less than 2-3 nm) MNPs. The diffraction lines of pure palladium should appear at s values higher than those of the corresponding signals of gold, due to its shorter lattice parameters (\(\mathrm{a_{Pd}}\) = 3.8898 A [43]). As the signals from an alloy fall in between the Bragg peaks of the pure metals, the position of this halo is compatible with a small-sized Pd-Au bimetallic alloy phase. The presence of a population of MNPs characterized by a size smaller than 3 nm is confirmed by the TEM images (see Supporting Information, Figure S1) showing the co-existence of both large and small MNPs in agreement with the diffraction patterns. We can obtain quantitative information by fitting the difference patterns to pseudo-Voigt functions provided that the signal to noise ratio is adequate. We therefore analyzed the region around the (111) and (200) peaks, since in the higher angles' region (i.e., above the (200) peaks), the difference signals become too weak for a reliable quantitative analysis. The best fits, which are shown in Figure 3, are obtained assuming the presence of three different phases (hereafter referred to as A, B, and C). The first phase (A) features two relatively sharp contributions (Figure 3, orange-shaded peaks), so that we were able to constrain their positions to the same lattice parameter; moreover, they imposed  
Figure 2: A-XRD patterns for P50 and P75 (\(\mathrm{I_{F}}\), red curves; \(\mathrm{I_{N}}\): blue curves) as a function of the energy independent abscissa, s = sin(b)/\(\lambda\), at the Au \(\mathrm{I_{III}}\) edge (**a**) and the Pd K edge (**b**). The curves of the two specimens are vertically shifted for the sake of clarity and the vertical lines highlight the expected position (\(\mathrm{s_{hkl}}\) = 1/2\(\mathrm{d_{hkl}}\)) of Au\({}_{\mathrm{fcc}}\) diffraction lines (\(\mathrm{a_{Au}}\) = 4.079 Å). The difference curve for P75 is reported for comparative purposes in (**a**,**b**). The difference patterns, \(\Delta\)I, in the region of the (111) and (200) fcc diffraction lines calculated at the Au \(\mathrm{I_{III}}\) edge and Pd K edge are illustrated for both P50 and P75 in (**c**,**d**), respectively. the same half-width and their intensity ratio was fixed to the I\({}_{200}\)/I\({}_{111}\) value (about 0.49) of the (111) and (200) reflections of pure fcc gold. In this way, we reduced the number of refinable parameters, thus improving the reliability of the fitting procedure. For the second and third phases (B and C, respectively), only a single contribution in the region of the (111) reflection is required to achieve the best fit (Figure 3, blue- and green-shaded peaks, respectively). These contributions are much broader than the corresponding ones for phase A and they are positioned towards higher values of s. Accordingly, they can be associated to phases which are richer in palladium and composed of smaller MNPs in comparison with phase A. The (200) peaks expected for the phases B and C are observed as a tailing in the difference patterns at high s values; they can be simply accounted for by a single further contribution, which falls in the region where the (200) reflections of phases B and C should be observed, but it is not specifically attributed to any of them. Figure 3 shows that there is a strong similarity between P50 and P75 samples at both Au and Pd edges. For both P50 and P75, one diffraction peak (the narrowest, A) is found almost coincident with that of pure gold (111). A second peak is observed in a position, which is in between those of pure gold (111) and pure palladium (111). The third one is found very close to that of pure palladium (111).