## 3 Results and Discussion
### Pigment Analysis
#### 3.1.3 Mineralogical and Chemical Compositions of the Red Topcoat  
The EDS analysis of the red topcoat is suggestive of a Fe-based pigment such as an ochre possibly mixed with calcium carbonate. The common contributing elements detected in the red layer were Fe, Ca, Al, and Si (Table S6, see Supplementary Material). If the red pigment within the artists' palette of Heddal and Eidsborg were comparable, the EDS analysis would display similar semi-quantitative results. However, the results from EDS and FT-IR analysis are varying. However, by using a multi-analytical approach these differences were characterized. The main difference between the IR spectra from Heddal and Eidsborg was found in the features attributed to clay minerals (Figure 5 and Table S13 in Supplementary Material). FT-IR spectroscopy of the Heddal samples permitted the identification of kaolinite (Al\({}_{2}\)(OH)\({}_{4}\)Si\({}_{2}\)O\({}_{5}\)), thanks to the presence of four specific peaks located between \(\sim\)3620 and \(\sim\)3700 cm\({}^{-1}\). These four features, in the OH region, represent a peculiar characteristic of kaolinite and are due to stretching motions of the inner groups situated between the tetrahedral and octahedral layers (\(\sim\)3620 cm\({}^{-1}\)) and on the octahedral surfaces [44]. The octahedral layers and surfaces tend to form hydrogen bonds with the oxygen atoms of the subsequent layer and lead to in-phase symmetric stretching vibrations (\(\sim\)3695 cm\({}^{-1}\)) and to out-of-plane stretching motions (\(\sim\)3669 and \(\sim\)3653 cm\({}^{-1}\)). Whereas spectra of Eidsborg specimens showed features compatible with the presence of clay minerals whose attribution to a specific phase was not plausible, as only a few broad bands were identified. Except for kaolinite and dickite, FT-IR spectra of clay minerals are often not specific in the spectral interval between 850 and 1150 cm\({}^{-1}\), frequently displaying one or two broad absorption bands. Additionally, in samples from both churches, a shoulder possibly related to small amounts of montmorillonite was found around 848-850 cm\({}^{-1}\)[44], as well as quartz which is generally indicated by the typical doublet at 779-800 cm\({}^{-1}\)[45] with the main band often masked by other very intense signals. Some of the FT-IR spectra showed profiles differing from the common features obtained for the same typology of layer (e.g., red or white). This is the case of the red layer from E1c that displayed a pronounced broad band between 990 and 1290 cm\({}^{-1}\) (Figure S6, see Supplementary Material). Such spectral regions host features compatible with those of a sulphate (983, 1087, 1116 and 1182 cm\({}^{-1}\)), probably barite (BaSO\({}_{4}\)) to which the two uncertain peaks at 611 and 638 cm\({}^{-1}\) also seem to be attributable. The semi quantitative analysis of XRD patterns of the red layers showed the presence of barite in E1d and E1e (Figure 6). Since XRD and FT-IR analysis were performed on different portions of samples (whole flakes for XRD and manually separated layers for FT-IR), a slight mismatch of results is possible. However, the recognition of barite features with two different techniques, in samples from the same church wall (Figure 3c), can be considered as a reliable indicator of its presence. Here, barite could be present as a natural impurity, as its appearance as an artist's pigment (i.e., barytes) occurred over a century after the rendering of this polychrome wall [46]. Additionally, a couple of other alteration phases were individuated from the diffraction pattern. Small amounts of anhydrite (CaSO4) and arcanite (K2 SO4) were detected, and their presence can be accredited to interactions with environmental pollutants. Most of the XRD analysis gave evidence of the occurrence of minerals, such as calcite and quartz, in samples from both Eidsborg and Heddal (Figure 6c,d). However, analysis showed a significant difference between the red pigment used within the two sites.