## 3 Results and Discussion  
### Penetration Depth and Distribution of the Polymer in the Pore Network  
Several SEM micrographs of each cross section were acquired and for each of them, two spots were analysed for the determination of the elemental composition. Two representative analyses are reported in Figure 1.  
The SEM micrographs revealed morphological features of the stone's porosity, which is mainly constituted by connected pores of hundreds of microns in size. The presence of protective agents is not visible, thus making it impossible to gain evidence about their distribution inside the pore network and their penetration depth. The EDS spectra of all stone spots show the signals of calcium, silicon, oxygen, carbon, potassium and chlorine, which can be attributed to calcite, quartz and feldspars [12], and the signal of fluorine, which is related to the presence of the protective agents, observed inside the pores. Perpendicular profiles of the stone section were analysed by soft X-ray microscopy. The emitted X-rays were acquired from areas at different depths from the surface and the fluorine peak area was used to evaluate if the two fluorinated compounds penetrated the stone (Figure 2). Figure 1: SEM micrographs with respective EDS spectra obtained for stone treated with Fluoline HY (**top**) and Fluo AQ (**bottom**). The coloured points indicate the spots where the EDS analysis was performed. The colour of the border for the EDS spectra and the atomic concentration results of spectra data analysis correspond to the spot colour. Figure 2: Fluorine peak area counts detected along the deepness profile of the two cross-sections. No particular trend is observed for both profiles, and the signal variation of the fluorine area seems to indicate that the protective agents penetrate into the inner part of the stone in a non-preferential way, due to the pore distribution, probably due to the partial accumulation of the polymers in inhomogeneous empty spaces. On the other hand, other similar protective agents were preferentially accumulated on the first 20 micrometres of the surface of marble [25] and 4 millimetres of the surface of calcarenite [26]. To deepen the spatial distribution of the protective, some representative XRF maps containing the spots at high fluorine content were acquired. The spot size was chosen as 1 \(\upmu\)m in diameter as a compromise between the features of interest and being compatible with the suitable XRF emitted signal. The obtained XRF maps are reported in Figure 3.  
The signal of oxygen refers to the stone's contribution (due to calcite and quartz), while the scattering accounts for the stone and the nano-micro-agglomerate's contribution. The area where both F and O signals are low corresponds to empty cavities and/or holes. The map of Fluo AQ shows that fluorine is mostly distributed along the pore's surface, while that of Fluoline HY evidences the formation of lumps with a poorly defined distribution inside the calcarenite porosity. In order to better understand the distribution of the protective Fluoline HY inside the calcarenite matrix, a bigger map at the energy of 2 keV was acquired. With this approach, the number of visible elements was improved, allowing us to see some characteristic stone  
Figure 3: Elemental XRF maps (acquired at 1 keV with 1.2 \(\upmu\)m diameter beam size, over an area of \(80\times 80\)\(\upmu\)m\({}^{2}\)) obtained for Cusa’s stone treated with Fluoline HY (**top**) and Fluo AQ (**down**). The scale bar is 20 \(\upmu\)m.  
elements, such as Al and Si. Several maps were acquired in sequence in order to obtain an overview of a wide area. The result of the mapping is reported in Figure 4.  
The high-energy maps emphasize the quartz grains through silicon signals, the feldspar correlated to aluminium and the oxygen signal in the other area can be attributed to the calcite grain. The fluorine distributes in small lumps inside the empty spaces between the grains.