## 3 Results and Discussion  
The film composition was confirmed by RBS analysis in agreement with the nominal values for Si, Zr and Yb. The Ag concentration depth profile (see examples in Figure 1) revealed a reduction from about 2 mol% (at surface) to 1 mol% (inner part of the film) both for the Ag-exchanged and the annealed samples. This indicates a small silver mobility in the glass ceramic matrix. Figure 1 presents the RBS spectra for the undoped samples before and after Ag-exchange, and the RUMP simulation of the latter (Figure 1a). In Figure 1b, a selected region corresponding to the Zr and Ag signals is reported, including a depth profile scale for the Zr signal, obtained from the RBS signal combined with the weighted average molar density between silica and zirconia, as described in the Experimental section. In Figure 1c, the calculated Ag depth profiling is reported for the samples GC0A, GC0B and GC0C-Post-exchange heat treatment changes only slightly the Ag profile, with no difference between sample GC0B and GC0C, within the experimental uncertainty of the RBS. Figure 1: Full Rutherford backscattering spectrometry (RBS) spectra (**a**) and selected spectral region corresponding to Zr and Ag (**b**) for undoped samples before and after Ag-exchange (GC0 and GC0A). Ag concentration profile (**c**) as a function of film depth for samples GC0A, GC0B and GC0C. The RUMP code simulation of the GC0A spectrum is shown. In (b), the corresponding film depth is reported for the Zr signal. XRD reflections before Ag\({}^{+}\)\(\leftrightarrow\)Na\({}^{+}\) ion exchange are reported in Figure 2, showing the presence of ZrO\({}_{2}\) tetragonal nanocrystals in the undoped samples and cubic nanocrystals in Yb-doped films, attested by a double peak (tetragonal) or a single peak (cubic) at 20 \(\approx\) 35.5\({}^{\circ}\) and 20 \(\approx\) 75\({}^{\circ}\). Noteworthy, deeper analysis which goes beyond the scope of this paper can be further exploited to corroborate the observed structural behavior and to quantify the relative phases [41]. The effect of Ag-exchange and subsequent annealing was not observed on XRD spectra. Indeed, it should be noted that crystal formation in similar materials occurs at 1000 \({}^{\circ}\)C. Previous studies highlighted that below that temperature, the sol-gel remains in a glassy state (see, for example, [PERSON] et al. [19]). Ag-exchange and the following annealing processes were done at 350 \({}^{\circ}\)C and up to 430 \({}^{\circ}\)C. Therefore, it can be reasonably concluded that the energies involved at these treatment temperatures are not enough for modifying the crystalline features of the glass-ceramic material. Finally, proper line broadening analysis (LBA) of XRD diffraction peaks [40] obtained by the Warren-Averbach method showed that nanocrystal size was about 14 nm for tetragonal zirconia in our undoped samples (GC0), and about 12 nm for cubic zirconia in Yb-doped samples (GC4). It is known from previous studies that the optical properties of silver-doped silicate glasses have broad luminescence emissions under UV light [42; 43; 44; 45] related to isolated Ag\({}^{+}\) ions (Em. 330-370 nm), Ag\({}^{+}\)-Ag\({}^{+}\) pairs (Em. 430-450 nm), formation of (Ag\({}_{3}\))\({}^{2+}\) trimers, multimers, and aggregates (Em. 550-650 nm and above). Studies of the PL emission under 280 nm excitation before (GC0) and after Ag-exchange (GC0A) and 430 \({}^{\circ}\)C annealing (GC0C) have been reported elsewhere [32], showing a main peak at 425 nm, reasonably related to Ag\({}^{+}\)-Ag\({}^{+}\) pairs, with a broad emission extending to the red spectral region, attributed to trimers and multimers. The modification of the curves after annealing is related to the evolution of the Ag species within the material. After annealing, the maximum peak at 425 nm slightly decreases, while the red emission contribution increases as a consequence of the decreasing of the number of dimers towards the formation of multimers and small aggregates.