## 2 Materials and Methods
### Results of Samples ZrN H, ZrN L, ZrN M and ZrN N
The analyses were carried out using an x-ray diffraction system (XRD, EMPYREAN, PAN analytical) equipped with a copper anode (40 kV\(\backslash\)40 mA). XRD apparatus was set up in a particular geometrical configuration which assures an intense monochromatic beam for a good signal-to-noise ratio and allows us to operate in a parallel-beam geometry suitable for asymmetrical and symmetrical reflection measurements. The phase identification was performed according to the well-known reference databases JCPDSICDD 2000. The experimental features compared with the database assessed the presence of a NaCl-like cubic structure for the ZrN films. A cascade graph displayed in Figure 10 (left and right) shows the comparison for N 1s and Zr 3d lines, respectively. The acquired data give evidence of the formation of a unique chemical environment for the three samples, presenting the main peaks in the same position. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{1}{c}{**Sample**} & \multicolumn{1}{c}{**N/Zr**} & \multicolumn{1}{c}{**Value of**} & \multicolumn{1}{c}{**Value of**} & \multicolumn{1}{c}{**N/Zr**} & \multicolumn{1}{c}{**Value of**} & \multicolumn{1}{c}{**Value of**} \\
**ID/Level from** & **SLG (30) \({}^{*}\)** & **Residual STD** & **Residual STD** & **LA (a,b,c) \({}^{*}\)** & **Residual STD** & **Residual STD** \\
**Surface** & **Fit Funct.** & **for Zr 3d \({}^{*}\)** & **for N 1s \({}^{*}\)** & **Fit Func.** & **for Zr 3d \({}^{**}\)** & **for N 1s \({}^{**}\)** \\ \hline ZrN L & 1.08 & 2.168 & 0.6242 & 0.81 & 1.890 & 1.023 \\ level 2 & & & & & & \\ ZrN L & 1.09 & 2.894 & 0.7336 & 0.87 & 2.356 & 1.167 \\ level 3 & & & & & & \\ ZrN L & 1.19 & 2.563 & 0.7098 & 0.87 & 1.794 & 1.065 \\ level 4 & & & & & & \\ ZrN L & 1.18 & 2.739 & 0.7779 & 0.84 & 1.883 & 0.917 \\ level 5 & & & & & & \\ ZrN M & 1.10 & 2.75 & 1.008 & 1.16 & 1.557 & 1.205 \\ level 2 & & & & & & \\ ZrN M & 1.13 & 2.868 & 1.176 & 1.10 & 1.488 & 1.187 \\ level 3 & & & & & & \\ ZrN M & 1.32 & 2.636 & 1.21 & 1.09 & 1.656 & 1.22 \\ level 4 & & & & & & \\ ZrN M & 1.05 & 2.456 & 1.142 & 1.05 & 1.345 & 1.373 \\ ZrN N & & & & & & \\ ZrN N & & & & & & \\ ZrN N & & & & & & \\ level 5 & & & & & & \\ \hline \hline \end{tabular} \({}^{**}\) refers to the SLG (30) fit function and is recalled in the respective coloumns “Value of residual STD for Zr 3d and N 1s”, while \({}^{*}\) refers to LA (a,b,c) Fit Function for the correspondent two last coloumns labels.  
\end{table} 
Table 4: ZrN samples quantitative results. The formation of ZrN was associated also with sample ZrN H, whose fits of Zr 3d and N1s are reported in Figure 11a,b, respectively. The main output parameters after fit (i.e., Zr 3d peak positions, main doublet distance \(\Delta\) = 2.5 eV, N1s peak position centered at 397.40 eV) confirmed, also for sample ZrN H, the formation of the ZrN compound. Results and Considerations about Satellite Peaks of High Resolution Zr 3d in All Samples Investigated  
Although 53 years have passed since the first publication about TiC and VC satellite structure [25], many questions still remain [26]. As correctly stated in the literature [25], shake-up satellites in core-electron spectra of transition-metal complexes result from a charge-transfer transition after the photoelectron ejection, and if charge transfers are observed in the absorption spectra, they will appear also on XPS spectra, as long as allowed by the selection rules. A further difficulty comes from the nature of the metal and the ligands and the symmetry of the structure under consideration. Moreover, when the overlapping of the satellite peak with a photoelectron line (or spectral feature) occurs, the solution of the  
Figure 11: Zr 3d, (**a**) and N 1s (**b**) fitted regions at level 5 from the surface, after Ar+ in situ sputtering of sample H.  
Figure 10: Comparison of N 1s (left) and Zr 3d (right) XPS regions, for the under-surface region (level 2), for the three different stoichiometric ZrN coatings: ZrN L, ZrN M and ZrN N.  
puzzle becomes very difficult to reconstruct.