## 2 Results and Discussion
Phase B is comprised of smaller MNPs, with diameters of about 3.3 nm for P50 and 5.6 nm for P75, while phase C is formed of tiny MNPs slightly larger than 1 nm. From the A-XRD analysis, the highest MNPs size is 16 nm, but TEM also shows the presence of even larger MNPs (tens of nm in diameter). However, according to HREM \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **P75** & & & **P50** & \\ \hline
**Phase** & **A** & **B** & **C** & **A** & **B** & **C** \\ \hline \multirow{2}{*}{**Edge**} & Pd & Pd & Pd & Pd & Pd & Pd \\  & Au & Au & Au & Au & Au & Au \\ \hline \multirow{2}{*}{**a (Å)**} & 4.077 & 4.000 & 3.920 & 4.065 & 4.042 & 3.905 \\  & 4.072 & 4.000 & 3.920 & 4.070 & 4.024 & 3.930 \\ \hline \multirow{2}{*}{**D (nm) a**} & 16.0 & 5.4 & 1.1 & 11.0 & 3.3 & 1.2 \\  & 15.7 & 5.8 & 1.0 & 11.0 & 3.2 & 1.3 \\ \hline \multirow{2}{*}{\(\chi^{\text{Au}}\) **(\%) b**} & 0.994 & 0.659 & 0.001 & 0.931 & 0.812 & 0.085 \\  & 0.966 & 0.659 & 0.001 & 0.956 & 0.859 & 0.087 \\ \hline \multirow{2}{*}{**A\({}_{\text{III}}\) (\%) c**} & 21 & 5 & 74 & 13 & 24 & 63 \\  & 12 & 4 & 84 & 8 & 22 & 70 \\ \hline \end{tabular}  
* from the Scherrer analysis; b atomic percentage of gold from the Vegard law; c relative area of the 111 deconvoluted peak.  
\end{table} 
Table 1: Analysis of the A-XRD difference patterns. a, D, and %Au are the lattice parameter, the size, and the Au content, respectively, of the identified metal phases (A, B, C) from the (111) diffraction peak. characterization, they are multi-twinned clusters (see Supporting Information, Figure S2) featured by several ordered domains, each one responsible for a single XRD signal [44]. The number of MNPs in each phase cannot be exactly assessed from the TEM data since sampling in the TEM is necessarily partial and the relevant results could not be fully representative. Moreover, the MNPs' size of phases B and C are pretty close to each other and it is difficult to trace a boundary between their populations. However, the A-XRD analysis provided both the size and the composition of MNPs for each phase so that the relative abundances of MNPs could be calculated. In addition, A-XRD analysis was carried out on macroscopic amounts (mg scale) of the samples and its results are therefore representative of the whole material. Using the information derived from A-XRD data for each phase (MNP diameter in nm and a in A), we calculated first the volume of the MNP \(\left(V_{MNP}~{}=~{}\frac{\pi}{6}\cdot D^{3}\right)\), supposed to be roughly spherical and to possess the fcc lattice, and then the number of atoms per MNP \(\left(N_{MNP,i}~{}=~{}4\cdot\frac{V_{MNP,i}}{a^{3}}\cdot 10^{-3};i~{}=~{}A,B,C\right)\). We also calculated the relative numbers of MNP belonging to A, B, and C \(\left(P_{MNP,i}~{}=~{}10^{6}\cdot\frac{A_{111,i}}{V_{MNP,i}}\sum\frac{A_{111,i }}{V_{MNP,i}};i~{}=~{}A,B,C\right)\), which should be proportional to the volume fractions of the respective phases, upon dividing the relative areas of the deconvoluted 111 peaks by V\({}_{\text{MNP}}\). These will be hereafter referred to as the \"volume adjusted populations\" (VAPs). From these values and from the atomic composition of each phase, the relative numbers of gold and palladium atoms in the two specimens were easily achieved as \(N_{M,i}~{}=~{}P_{MNP,i}\cdot N_{M,MNP,i}\cdot x_{M,i};M=Au,Pd;i~{}=~{}A,B,C\). This provided two values (one for each edge) of the atomic (molar) ratio between palladium and gold for P50 and P75, which are reported in Table 2. The values of N\({}_{\text{Pd}}\)/N\({}_{\text{Au}}\) from the palladium edge and the gold edge of P50 are in good to excellent agreement with the experimental value of 1.85 mol-mol\({}^{-1}\). For P75, the agreement of the single values is not as good, but the average, 5.10, is not far from the 5.56 value obtained from the metal analysis.