## 3 Results
### Palladium Displacement Plating Characterization  
Due to the very low amount of palladium deposited with the PDP method, SEM-EDS analysis was used to measure the film thickness. The EDS spectra of the specimens made of copper with various thicknesses of palladium were simulated using NIST DTSA-II software. From the spectra, the K-ratio was calculated to build a calibration curve (Figure 2) [43; 44]. K-ratios were defined as the ratio between the peak intensity (X-ray counts) for the element of interest in the sample and the peak intensity of the pure element at the same energy. Then, the spectra of our real samples were recorded, the K-ratio was calculated and the thickness was obtained by means of the calibration curve. The calibration curve for the thickness determination was built simulating the following thicknesses of palladium on copper: 0 nm, 5 nm, 10 nm, 20 nm, 50 nm, and 75 nm (Figure 2 inset). The simulated points are not equally spaced because the correlation between thickness and K-ratio is exponential; in this way, the fitting is more reliable and optimized, keeping the number of points low. For low metal thicknesses, the correlation between the K-ratio and the thickness values can be approximated by a second-grade equation which provides a simpler regression maintaining a high reliability (R\({}^{2}\) > 0.999). Figure 1: Aesthetic appearance of palladium films obtained by displacement plating. Sample numbers are reported on the uncoated part of each sample. The thicknesses obtained with the K-ratios through the calibration curve are reported in Table 4. The standard deviation was calculated from the values provided by the EDS spectra. From the results obtained, comparing the same deposition solution, an increase in deposition time seemed to act in a more relevant way than the presence or the absence of stirring did on the obtained thickness. Although the presence of stirring also contributed to increasing the Pd thickness, guaranteeing a constant concentration of Pd ions at the substrate-solution interface. EDS analysis did not detect the presence of Pd in sample #3. For this reason, in Table 4, the K-ratio and the thickness values are 0. OM was used to verify the absence or presence of discontinuities and defects due to an incomplete coverage of the copper substrate. Samples #6, #8, and, #10 were observed using optical microscopy. These three samples were selected because they were the best results obtained from each deposition solution (A, B, and C) in terms of macroscopical homogeneity and palladium thicknesses measured using the K-ratio method. OM images of samples #6, #8, and #10 are reported in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **K-Ratio** & **EDS Thickness (nm)** & **Std. Dev. (\(\pm\)nm)** \\ \hline \#1 & 0.006 & 1.7 & 0.3 \\ \#2 & 0.015 & 4.2 & 0.3 \\ \#3 & 0.000 & 0 & / \\ \#4 & 0.003 & 0.8 & 0.3 \\ \#5 & 0.039 & 10.6 & 0.3 \\ \#6 & 0.084 & 22.2 & 0.2 \\ \#7 & 0.010 & 2.8 & 0.3 \\ \#8 & 0.034 & 9.3 & 0.3 \\ \#9 & 0.004 & 1.1 & 0.3 \\ \#10 & 0.022 & 6.1 & 0.3 \\ \#11 & 0.070 & 18.6 & 0.2 \\ \#12 & 0.168 & 41.7 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Equivalent thickness results obtained by EDS spectra of palladium displacement plating samples. Figure 3: Optical microscopy images of samples (**a**) #6; (**b**) #8, and (**c**) #10 after palladium displacement deposition. Comparing the three different samples from an optical microscopy point of view, the surfaces resulted in being sufficiently homogeneous and compact, as could be seen by observing the samples with the naked eye. The presence of small bumps and scratches (Figure 3) was attributed to the imperfections present on the copper substrate and not to the palladium deposition.