## 3 Results and Discussion
Thus, heat treatment at 500 \({}^{\circ}\)C induced out-diffusion of silver ions to the glass surface with formation of SNIF, resulting in a 95% reduction in the total number of silver ions in the PTR-M glass sample compared to the nontreated ion-exchanged sample. XRD analysis of the PTR glass samples heat-treated at different temperatures for 3 h revealed characteristic peaks for metallic silver (Figure 5), confirming that the observed SNIF consisted of silver nanoparticles. SEM analysis of the of the ion-exchanged and heat-treated PTR-M glass surface revealed the presence of isolated nanometer and micrometer particles (Figure 6). SNIF formed at 350 \({}^{\circ}\)C consisted of nanoparticles of different shapes (triangle, square, and rectangular), while, at higher temperatures, nanoparticles had only spherical shape. The latter should be related to the melting of small SNPs during the heat treatment at temperatures above 400 \({}^{\circ}\)C [38; 39; 40]. Moreover, SEM analysis showed that the mean diameter of silver particles in the SNIF increased from 140 to 320 nm with heat treatment temperature increasing from 350 to 500 \({}^{\circ}\)C. This result correlates with  
Figure 3: Absorbance spectra of PTR-M glass sample after the Na\({}^{+}\)–Ag\({}^{+}\) IE and with SNIF obtained at 350 \({}^{\circ}\)C (**a**), 400 \({}^{\circ}\)C (**b**), 450 \({}^{\circ}\)C (**c**), and 500 \({}^{\circ}\)C (**d**) for different durations, indicated by colors. the changes in absorbance spectra presented in Figure 3. The phase retardation of the electromagnetic field inside large particles led to the plasmon modes of higher multipole orders (quadrupolar, octupolar, and hexadecapolar) observed in the spectra [41]. Considering possible mechanisms of the spontaneous growth of SNIF on the ion-exchanged PTR glass surface, the main question concerns the source of electrons for reducing silver ions. The mechanism of silver ion reduction by water vapor in a wet argon atmosphere responsible for growth of SNIF on the surface of Na+-Ag+ ion-exchanged borosilicate glass was suggested by [PERSON] et al. [42]. The authors proposed silver-proton exchange with the formation of silver oxide that thermally decomposes further to silver and oxygen. \[\equiv\mathrm{Si-O-Ag^{+}}+\frac{1}{2}\mathrm{H_{2}O}\leftrightarrow \equiv\mathrm{Si-O-H^{+}}+\frac{1}{2}\mathrm{Ag_{2}O}. \tag{1}\]  
\[\mathrm{Ag_{2}O}\to 2\mathrm{Ag^{0}+O}. \tag{2}\]  
Other routes of silver reduction by glass impurities or nonbridging oxygen can be excluded considering that they would lead to coloration due to growth of SNPs inside the glass [43]. Thus, we suggest that SNIF on the surface of Na+-Ag+ ion-exchanged PTR glass surface growth is the result of interaction with the water molecules always present in air. Figure 4: (**a**) Absorbance spectra of as-synthesized and Na+-Ag+ ion-exchanged PTR-M glass samples after heat treatment at 500 °C for different durations measured after removing the SNIF. (**b**) The differential absorbance spectra obtained by subtracting the spectrum of the as-synthesized sample from the others. Figure 5: XRD spectra of the ion-exchanged and heat-treated for 3 h PTR-M glass samples with SNIF. However, further research is needed to clarify the exact mechanism responsible for the growth of SNIF. A drop (\(\sim\)5 mm in diameter) of 8 \(\times\) 10\({}^{-7}\) mol/L R6G aqueous solution was deposited on the samples to investigate SERS-active properties of silver films on the surface of the PTR-M glass. The Raman spectra were measured after drying the R6G drop with the confocal Raman microscope (Renibaw); a red laser beam (633 nm) was focused at the sample surface with a 50\(\times\)/0.55 micro-objective. A significantly enhanced spectrum was observed at surface with SNIF compared to pristine PTR-M glass (Figure 7a). As growth of SNIF on the PTR glass is a diffusion process, it can be grown using the same substrate in several cycles of thermal treatment and mechanical removal.